task_id stringlengths 12 19 | prompt stringlengths 944 53.4k |
|---|---|
statistic::St000001 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of reduced words for a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
si... |
statistic::St000002 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of occurrences of the pattern 123 in a permutation.
Collection: Permutations
Collection definition:
A
p... |
statistic::St000003 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of
Collection: Integer partitions
Collection definition:
An
integer partition
$\lambda$
of
$n \in \math... |
statistic::St000004 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The major index of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$
is a b... |
statistic::St000005 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The bounce statistic of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semilength
$n$
i... |
statistic::St000006 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The dinv of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semilength
$n$
is a lattice ... |
statistic::St000007 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of saliances of the permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
... |
statistic::St000008 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The major index of the composition.
Collection: Integer compositions
Collection definition:
An
integer composition... |
statistic::St000009 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The charge of a standard tableau.
Collection: Standard tableaux
Collection definition:
A
standard (Young) tableau
... |
statistic::St000010 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The length of the partition.
Collection: Integer partitions
Collection definition:
An
integer partition
$\lambda$
... |
statistic::St000011 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of touch points (or returns) of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
... |
statistic::St000012 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The area of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semilength
$n$
is a lattice ... |
statistic::St000013 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The height of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semilength
$n$
is a lattic... |
statistic::St000014 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of parking functions supported by a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck pat... |
statistic::St000015 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of peaks of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semilength
$n$
is... |
statistic::St000016 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of attacking pairs of a standard tableau.
Collection: Standard tableaux
Collection definition:
A
standa... |
statistic::St000017 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of inversions of a standard tableau.
Collection: Standard tableaux
Collection definition:
A
standard (Y... |
statistic::St000018 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of inversions of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$... |
statistic::St000019 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The cardinality of the support of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
... |
statistic::St000020 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The rank of the permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$
is a biject... |
statistic::St000021 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of descents of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$... |
statistic::St000022 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of fixed points of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size... |
statistic::St000023 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of inner peaks of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
... |
statistic::St000024 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of double up and double down steps of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck... |
statistic::St000025 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of initial rises of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semilengt... |
statistic::St000026 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The position of the first return of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semi... |
statistic::St000027 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The major index of a Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semilength
$n$
is a l... |
statistic::St000028 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of stack-sorts needed to sort a permutation.
Collection: Permutations
Collection definition:
A
permutat... |
statistic::St000029 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The depth of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$
is a bijecti... |
statistic::St000030 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The sum of the descent differences of a permutations.
Collection: Permutations
Collection definition:
A
permutatio... |
statistic::St000031 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of cycles in the cycle decomposition of a permutation.
Collection: Permutations
Collection definition:
... |
statistic::St000032 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of elements smaller than the given Dyck path in the Tamari Order.
Collection: Dyck paths
Collection def... |
statistic::St000033 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of permutations greater than or equal to the given permutation in (strong) Bruhat order.
Collection: Per... |
statistic::St000034 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The maximum defect over any reduced expression for a permutation and any subexpression.
Collection: Permutations
C... |
statistic::St000035 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of left outer peaks of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
... |
statistic::St000036 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation.
Co... |
statistic::St000037 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The sign of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$
is a bijectio... |
statistic::St000038 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The product of the heights of the descending steps of a Dyck path.
Collection: Dyck paths
Collection definition:
A... |
statistic::St000039 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of crossings of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n... |
statistic::St000040 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of regions of the inversion arrangement of a permutation.
Collection: Permutations
Collection definitio... |
statistic::St000041 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of nestings of a perfect matching.
Collection: Perfect matchings
Collection definition:
A
perfect match... |
statistic::St000042 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of crossings of a perfect matching.
Collection: Perfect matchings
Collection definition:
A
perfect matc... |
statistic::St000043 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of crossings plus two-nestings of a perfect matching.
Collection: Perfect matchings
Collection definiti... |
statistic::St000044 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of vertices of the unicellular map given by a perfect matching.
Collection: Perfect matchings
Collectio... |
statistic::St000045 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of linear extensions of a binary tree.
Collection: Binary trees
Collection definition:
A
binary tree
is... |
statistic::St000046 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given part... |
statistic::St000047 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of standard immaculate tableaux of a given shape.
Collection: Integer compositions
Collection definitio... |
statistic::St000048 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The multinomial of the parts of a partition.
Collection: Integer partitions
Collection definition:
An
integer part... |
statistic::St000049 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of set partitions whose sorted block sizes correspond to the partition.
Collection: Integer partitions
... |
statistic::St000050 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The depth or height of a binary tree.
Collection: Binary trees
Collection definition:
A
binary tree
is a rooted tr... |
statistic::St000051 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The size of the left subtree of a binary tree.
Collection: Binary trees
Collection definition:
A
binary tree
is a ... |
statistic::St000052 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of valleys of a Dyck path not on the x-axis.
Collection: Dyck paths
Collection definition:
A
Dyck path
... |
statistic::St000053 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of valleys of the Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyck path
of semilength
$n... |
statistic::St000054 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The first entry of the permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$
is a... |
statistic::St000055 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The inversion sum of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$
is a... |
statistic::St000056 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The decomposition (or block) number of a permutation.
Collection: Permutations
Collection definition:
A
permutatio... |
statistic::St000057 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The Shynar inversion number of a standard tableau.
Collection: Standard tableaux
Collection definition:
A
standard... |
statistic::St000058 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The order of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$
is a bijecti... |
statistic::St000059 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The inversion number of a standard tableau as defined by Haglund and Stevens.
Collection: Standard tableaux
Collec... |
statistic::St000060 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The greater neighbor of the maximum.
Collection: Permutations
Collection definition:
A
permutation
of
size
$n$
is ... |
statistic::St000061 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of nodes on the left branch of a binary tree.
Collection: Binary trees
Collection definition:
A
binary ... |
statistic::St000062 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The length of the longest increasing subsequence of the permutation.
Collection: Permutations
Collection definitio... |
statistic::St000063 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of linear extensions of a certain poset defined for an integer partition.
Collection: Integer partitions... |
statistic::St000064 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of one-box pattern of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
s... |
statistic::St000065 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of entries equal to -1 in an alternating sign matrix.
Collection: Alternating sign matrices
Collection ... |
statistic::St000066 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The column of the unique '1' in the first row of the alternating sign matrix.
Collection: Alternating sign matrices... |
statistic::St000067 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The inversion number of the alternating sign matrix.
Collection: Alternating sign matrices
Collection definition:
... |
statistic::St000068 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of minimal elements in a poset.
Collection: Posets
Collection definition:
A (finite)
poset
(or
partiall... |
statistic::St000069 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of maximal elements of a poset.
Collection: Posets
Collection definition:
A (finite)
poset
(or
partiall... |
statistic::St000070 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of antichains in a poset.
Collection: Posets
Collection definition:
A (finite)
poset
(or
partially orde... |
statistic::St000071 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of maximal chains in a poset.
Collection: Posets
Collection definition:
A (finite)
poset
(or
partially ... |
statistic::St000072 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of circled entries.
Collection: Gelfand-Tsetlin patterns
Collection definition:
Not available.
Encodin... |
statistic::St000073 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of boxed entries.
Collection: Gelfand-Tsetlin patterns
Collection definition:
Not available.
Encoding ... |
statistic::St000074 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of special entries.
Collection: Gelfand-Tsetlin patterns
Collection definition:
Not available.
Encodin... |
statistic::St000075 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The orbit size of a standard tableau under promotion.
Collection: Standard tableaux
Collection definition:
A
stand... |
statistic::St000076 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The rank of the alternating sign matrix in the alternating sign matrix poset.
Collection: Alternating sign matrices... |
statistic::St000077 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of boxed and circled entries.
Collection: Gelfand-Tsetlin patterns
Collection definition:
Not available... |
statistic::St000078 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of alternating sign matrices whose left key is the permutation.
Collection: Permutations
Collection def... |
statistic::St000079 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of alternating sign matrices for a given Dyck path.
Collection: Dyck paths
Collection definition:
A
Dyc... |
statistic::St000080 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The rank of the poset.
Collection: Posets
Collection definition:
A (finite)
poset
(or
partially ordered set
) is a... |
statistic::St000081 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of edges of a graph.
Collection: Graphs
Collection definition:
A (finite, undirected, simple)
graph
$G ... |
statistic::St000082 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of elements smaller than a binary tree in Tamari order.
Collection: Binary trees
Collection definition:... |
statistic::St000083 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of left oriented leafs of a binary tree except the first one.
Collection: Binary trees
Collection defin... |
statistic::St000084 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of subtrees.
Collection: Ordered trees
Collection definition:
An
ordered tree
is a rooted tree where th... |
statistic::St000085 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of linear extensions of the tree.
Collection: Ordered trees
Collection definition:
An
ordered tree
is a... |
statistic::St000086 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of subgraphs.
Collection: Graphs
Collection definition:
A (finite, undirected, simple)
graph
$G = (V,E)... |
statistic::St000087 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of induced subgraphs.
Collection: Graphs
Collection definition:
A (finite, undirected, simple)
graph
$G... |
statistic::St000088 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The row sums of the character table of the symmetric group.
Collection: Integer partitions
Collection definition:
... |
statistic::St000089 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The absolute variation of a composition.
Collection: Integer compositions
Collection definition:
An
integer compos... |
statistic::St000090 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The variation of a composition.
Collection: Integer compositions
Collection definition:
An
integer composition
$\a... |
statistic::St000091 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The descent variation of a composition.
Collection: Integer compositions
Collection definition:
An
integer composi... |
statistic::St000092 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of outer peaks of a permutation.
Collection: Permutations
Collection definition:
A
permutation
of
size
... |
statistic::St000093 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The cardinality of a maximal independent set of vertices of a graph.
Collection: Graphs
Collection definition:
A (... |
statistic::St000094 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The depth of an ordered tree.
Collection: Ordered trees
Collection definition:
An
ordered tree
is a rooted tree wh... |
statistic::St000095 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of triangles of a graph.
Collection: Graphs
Collection definition:
A (finite, undirected, simple)
graph... |
statistic::St000096 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of spanning trees of a graph.
Collection: Graphs
Collection definition:
A (finite, undirected, simple)
... |
statistic::St000097 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The order of the largest clique of the graph.
Collection: Graphs
Collection definition:
A (finite, undirected, sim... |
statistic::St000098 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The chromatic number of a graph.
Collection: Graphs
Collection definition:
A (finite, undirected, simple)
graph
$G... |
statistic::St000099 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of valleys of a permutation, including the boundary.
Collection: Permutations
Collection definition:
A
... |
statistic::St000100 | Write only Python code that defines `def solve(obj):`.
Do not include explanation, prose, tests, or Markdown.
The function must return an integer.
You may use the Python standard library only.
Task name: The number of linear extensions of a poset.
Collection: Posets
Collection definition:
A (finite)
poset
(or
partial... |
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