| {"id":"def:containment","label":"containment","background_color":"#A3D6FF","border_color":"blue","kind":"box","dep_graph_url":"https://YaelDillies.github.io/ForbiddenMatrix/blueprint/dep_graph_document.html","dependencies":[],"nlp_text":"An \\(n\\)-by-\\(m\\) binary matrix \\(M\\) contains an \\(n'\\)-by-\\(m'\\) matrix \\(P\\) if there are integers \\(1 \\leq i_1 \\leq \\ldots \\leq i_{n'} \\leq n\\) and \\(1 \\leq j_1 \\leq \\ldots \\leq j_{m'} \\leq m\\) such that for all \\(i' \\in [n'], j' \\in [m']\\), \\(P(i',j') = 1\\) implies \\(M(i_{i'},j_{j'}) = 1\\). If \\(M\\) does not contain \\(P\\), then \\(M\\) avoids \\(P\\).","doc_url":null,"latex_link":"chap-defs.html#def:containment","lean_link":null,"lean_decl_name":"containment","kind_description":"definitions","status_from_color":"ready_to_formalize","lookup_in_mathlib4v4.22.0":true,"found_in_mathlib4v4.22.0":false,"proof_status":"nlp_only"} |
| {"id":"def:extremal function","label":"extremal function","background_color":"#A3D6FF","border_color":"blue","kind":"box","dep_graph_url":"https://YaelDillies.github.io/ForbiddenMatrix/blueprint/dep_graph_document.html","dependencies":[],"nlp_text":"Given two integers \\(n,m\\), we denote \\(Ex(P,n,m)\\) as the maximum number of 1’s in a matrix avoiding a matrix \\(P\\). We also define \\(Ex(P,n) = Ex(P,n,n)\\).","doc_url":null,"latex_link":"chap-defs.html#def:extremal function","lean_link":null,"lean_decl_name":"extremal function","kind_description":"definitions","status_from_color":"ready_to_formalize","lookup_in_mathlib4v4.22.0":true,"found_in_mathlib4v4.22.0":false,"proof_status":"nlp_only"} |
