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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials minimal atom; Grothendieck category; Noetherian generator; compressible object
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck-Ogg-Shafarevich formula; Swan conductor; Lefschetz fixed point formula; Artin representation A. Abbès, The Grothendieck-Ogg-Shafarevich formula for arithmetic surfaces, Journal of Algebraic Geometry, 9 (2000), 529-576.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quantum special linear groups; quantum matrix bialgebras; rings of quantum coinvariants; quantum Grassmannians; presentations; quantum Schubert varieties; coactions R. Fioresi and C. Hacon, Quantum coinvariant theory for the quantum special linear group and quantum Schubert varieties. J. Algebra 242 (2001), 433-446.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials survey; topos; generalized space; represenation theorems; Grothendieck topos; locales; localic groups; groupoids; geometric morphisms; Barr's theorem; Freyd's theorem; étendue; covering theorems; exponential variety; topological group Peter T. Johnstone, How general is a generalized space?, Aspects of topology, London Math. Soc. Lecture Note Ser., vol. 93, Cambridge Univ. Press, Cambridge, 1985, pp. 77 -- 111.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials blow-ups; Hirzebruch surfaces; quartics with a double line; normality
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials conchoid; resultant; double planes Albano, A.; Roggero, M., Conchoidal transform of two plane curves, Appl. Algebra Eng. Commun. Comput., 21, 309-328, (2010)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials flat localizations of Abelian categories; structure presheaves of modules; quantized algebras; noncommutative schemes in categories; left spectrum; maximal left ideals; completely prime left ideals; categories of rings; Levitzki radical; quasi-affine schemes; projective spectra; quantized rings; quantum planes; algebra of \(q\)-differential operators; Weyl algebras; quantum envelopes; coordinate rings; generalized Weyl algebras; skew polynomial rings; Serre subcategories; Grothendieck categories; hyperbolic rings; skew PBW monads; monoidal category; Kac-Moody and Virasoro Lie algebras; semigroup-graded monads; Gabriel-Krull dimension Rosenberg, A.L.: Algebraic Geometry Representations of Quantized Algebras. Kluwer Academic Publishers, Dordrecht, Boston London (1995)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials discriminantly separable polynomials; integrable quad-equations; pencils of conics; Möbius transformations; two-valued groups Dragović, V. and Kukić, K., Discriminantly Separable Polynomials and Quad-Graphs, arXiv:1303.6534v1 (26 Mar 2013).
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck's motives; standard conjectures; Chow-Künneth decomposition; Bloch-Beilinson filtration; elliptic modular varieties Murre, J.: Lectures on motives. In: Müller-Stach, S., Peters, C. (eds.) Trancendental Aspects of Algebraic Cycles, London Math. Soc. Lecture Note Series, No: 133, pp. 123--170. Cambridge University Press, Cambridge (2004)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials configuration; pencil; double covers M. Artebani; I. Dolgachev, The Hesse pencil of plane cubic curves, L'Enseignement Mathématique. Revue Internationale. 2e Série, 55, 235-273, (2009)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials equivariant quantum cohomology; homogeneous spaces; Schubert Calculus; Gromov-Witten invariant DOI: 10.4310/MRL.2009.v16.n1.a2
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials finite fields; symmetric polynomials; singular locus; rational solutions; diagonal equations
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials supersingular elliptic curve; orthogonal polynomials from hyperelliptic series; supersingular polynomial; modular forms; Atkin orthogonal polynomials; congruence; recursion relation Kaneko, M., Zagier, D.: Supersingular \(j\)-invariants, hypergeometric series, and Atkin's orthogonal polynomials. In: Computational Perspectives on Number Theory (Chicago, IL, 1995). AMS/IP Stud. Adv. Math., 7, pp. 97-126. American Mathematical Society, Providence, RI (1998)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials real flag manifolds; symmetric group; root systems; Schubert cells; homology; height of roots; boundary coefficients
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials hyperbolic polynomials; perturbation theory; linear operators; eigenvalue; symmetric matrices; uniform diagonalization; antisymmetric matrices Kurdyka K., Paunescu L.: Hyperbolic polynomials and multiparameter real-analytic perturbation theory. Duke Math. J. 141(1), 123--149 (2008)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials finite fields; Reed-Solomon codes; deep holes; symmetric polynomials; singular hypersurfaces; rational points Cafure, A.; Matera, G.; Privitelli, M.: Singularities of symmetric hypersurfaces and Reed-Solomon codes. Adv. math. Commun. 6, No. 1, 69-94 (2012)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties; minuscule; Gorenstein
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials local intersection number of two curves; infinitely near points; intersection numbers; curve and its polar; duality; Schubert cycle Teissier, B.: Quelques points de l'histoire des variétés polaires, de Poncelet à nos jours, (1988)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials prevariety of locally convex spaces; Grothendieck ideal space; universal generator; stabilized base
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials rook length polynomial; projective variety; partition variety; Grassmannian manifold; flag manifold; Schubert cells; Bruhat order Ding, K., Rook placements and generalized partition varieties, Discrete Math., 176, 1-3, 63-95, (1997)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials rigid analytic spaces; étale cohomology; Artin-Grothendieck vanishing; comparison theorems
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schur polynomials; log-concavity; Lorentzian polynomials; weight multiplicities
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials multiplication by the class of a special Schubert variety; integral cohomology ring of the flag manifold; Pieri formual; Bruhat order Frank Sottile, Pieri's formula for flag manifolds and Schubert polynomials, Ann. Inst. Fourier (Grenoble) 46 (1996), no. 1, 89-110 (English, with English and French summaries).
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties; Cohen-Macaulay; arithmetically normal; projective embedding Brion, M.: Multiplicity-free subvarieties of flag varieties. Commutative algebra (Grenoble/Lyon, 2001), 13-23, Contemp. Math., \textbf{331}, Amer. Math. Soc., Providence, RI, 2003
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials semisimple Lie algebra; weight multiplicity; \(q\)-analogue; Hall-Littlewood polynomials; Kostant partition function Panyushev, D. I., Generalised Kostka-Foulkes polynomials and cohomology of line bundles on homogeneous vector bundles, Selecta Math. (N.S.), 16, 315-342, (2010)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials crystal basis; fixed point Lie subalgebra; Newton-Okounkov body; orbit Lie algebra; Schubert variety
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials generical description; minimal number of polynomials; sums of signs Bonnard, I., Description of algebraically constructible functions, Adv. Geom., 3, 145-161, (2003)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials split connected reductive groups; dominant coweights; affine Schubert varieties; equidimensional varieties; Springer resolutions; affine Grassmannians; Hecke algebras; structure constants; saturation Grothendieck, A., Diéudonné, J.: Éléments de Géométrie Algeébrique, IV: Étude locale ded schémas e des morphismes de schémas, Seconde partie, Inst.~ Hautes Études Sci.~Publ.~Math.~\textbf{24} (1965)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials plane curve singularities; \(\mu\)-constant stratum; \(b\)-exponents; Bernstein polynomials; improper integrals; residues E. Artal Bartolo, Pi. Cassou-Nogu`es, I. Luengo, and A. Melle-Hern'andez, Yano's conjecture for 2Puiseux pairs irreducible plane curve singularities, Publ. RIMS Kyoto Univ. 53 (2017), no. 1, 211--239. DOI: 10.4171/PRIMS/53-1-7
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quantum algebra of functions; semisimple algebraic group; Schubert variety; basis; gradations V. Lakshmibai and N. Reshetikhin. ''Quantum flag and Schubert schemes''. Deformation Theory and Quantum Groups with Applications to Mathematical Physics. Contemp. Math., Vol. 134. American Mathematical Society, 1992, pp. 145--181.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials unirationality of moduli space of 5-dimensional principally; polarized abelian varieties; Prym moduli space parametrizing double covers of curves of; genus 6; nets of quadrics; theta characteristic; Prym moduli space parametrizing double covers of curves of genus 6 R. Donagi, The unirationality of
\[
\mathcal{A}_{5}
\]
. Ann. Math. 119, 269--307 (1984)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials permutations; Schubert varieties
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Hilbert scheme; virtual Hodge polynomials; symmetric product J. Cheah, ''On the Cohomology of Hilbert Schemes of Points,'' J. Algebr. Geom. 5, 479--511 (1996).
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials semi-invariants of quivers; Schubert classes; Littlewood-Richardson coefficients; representations of quivers; Ringel bilinear forms Derksen, H., Schofield, A., Weyman, J.: On the number of subrepresentations of a general quiver representation. J. Lond. Math. Soc. (2) 76(1), 135--147 (2007)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials characteristic map; symmetric space; Macdonald polynomials
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Minkowski plane; relativistic conics; elliptic billiards; periodic trajectories; extremal polynomials; Chebyshev polynomials; Akhiezer polynomials; discriminantly separable polynomials
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials flag varieties; Schubert cell decomposition; \(M\)-property; configuration spaces; Mayer-Vietoris spectral sequence Shapiro B. Z., Topology Appl. 43 (1) pp 65-- (1992)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials authentication codes with secrecy; algebraic function fields; linearized polynomials Özbudak, E.K.; Özbudak, F.; Saygı, Z., A class of authentication codes with secrecy, Des. codes cryptogr., 59, 287-318, (2011)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials intersection theory of moduli spaces of curves; matroid Chow rings; polynomials of matroids
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck universe
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Geometric Galois actions; Grothendieck's esquisse d'un programme; Proceedings; Conference; Geometry; Arithmetic; Moduli spaces Leila Schneps and Pierre Lochak , Geometric Galois actions. 1, London Mathematical Society Lecture Note Series, vol. 242, Cambridge University Press, Cambridge, 1997. Around Grothendieck's ''Esquisse d'un programme''.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials topological triviality; modified Nash triviality; weighted homogeneous polynomials Koike, S., Modified Nash triviality theorem for a family of zero-sets of weighted homogeneous polynomial mappings, J. Math. Soc. Japan, 49, 617-631, (1997)
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert variety; rationally smooth; lookup conjecture
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double tangent; fourth order curves; conics; pencil of conics
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Galois theory; rings; modules; algebras; coverings; Riemann surfaces; categories; functors; Belyi polynomials; dessins d'enfants Régine Douady and Adrien Douady, Algèbre et théories galoisiennes. 1, CEDIC, Paris, 1977 (French). Algèbre. [Algebra]. Régine Douady and Adrien Douady, Algèbre et théories galoisiennes. 2, CEDIC, Paris, 1979 (French). Théories galoisiennes. [Galois theories].
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck ring; banana graphs; flower graphs
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials genus 3 curves; genus 4 curves; elliptic-hyperelliptic curve; Kummer variety; moduli spaces; étale double covers
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties Jones, B. F., \textit{singular Chern classes of Schubert varieties via small resolution}, Int. Math. Res. Not. IMRN, 2010, 1371-1416, (2010)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Chowla-Zassenhaus conjecture; cyclic polynomial; \(p\)th Chebyshev polynomial; extension of constants; branch cycle; Davenport polynomials Fried M D. Extension of Constants, Rigidity, and the Chowla-Zassenhaus Conjecture. Finite Fields Appl, 1995, 1: 326--359
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials complex tori; hyperelliptic manifolds; Bagnera-De Franchis manifolds; Hodge structures; cyclic coverings; group algebra; factorial rings; cyclotomic rings; resultants of cyclotomic polynomials; fundamental groups
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert subschemes; flag scheme; representation theory of infinitesimal algebraic groups Kaneda, M., On the Frobenius morphism of flag schemes, Pacific J. Math., 163, 315-336, (1994)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Heisenberg algebras; Hecke algebras; planar diagrammatics; finite general linear groups; Grothendieck groups; categorification A. Licata & A. Savage, ``Hecke algebras, finite general linear groups, and Heisenberg categorification'', Quantum Topol.4 (2013) no. 2, p. 125-185
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials enumerative geometry; Schubert variety; Pieri formula; Pieri homotopy algorithm; Pieri poset; algorithm Li D, Qi L, Zhou S (2002) Descent directions of quasi-Newton methods for symmetric nonlinear equations. SIAM J Numer Anal 40(5): 1763--1774
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck local residue symbol; toric variety; cohomology class; Dolbeault isomorphism D. Cox, ''Toric Residues,'' Ark. Mat. 34(1), 73--96 (1996).
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials strata of \(k\)-differentials; deformation theory; tautological classes; double ramification cycles Schmitt, J., Dimension theory of the moduli space of twisted \textit{k}-differentials
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double cover; quartic surface; intermediate Jacobian; rational threefold; conic bundle
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials cross ratio variety; rational double point; Weyl groups; Appell- Lauricella hypergeometric function; deformation of \(E_ 6\)-singularity; cubic surface; Cayley family J. Sekiguchi: The versal deformation of the \(E_6\)-singularity and a family of cubic surfaces , J. Math. Soc. Japan 46 (1994), 355--383.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double covers; basepoint-free pencils Luis Fuentes García, Pencils on double coverings of curves, Arch. Math. (Basel) 92 (2009), no. 1, 35 -- 43.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Kostka-Shoji polynomials; cohomology vanishing; quivers; Lusztig convolution diagram
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Fukaya-Seidel category; pretriangulated \(A_\infty\)-categories; derived category of singularities; Brieskorn-Pham polynomials
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grassmannians; equivariant \(K\)-theory; puzzle; Schubert calculus; Littlewood-Richardson rule O. Pechenik and A. Yong. ''Equivariant K-theory of Grassmannians II: The Knutson-Vakil conjecture''. 2015. arXiv:1508.00446.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Kostka polynomials; atomic decomposition; nilpotent conjugacy classes; nilpotent orbit varieties William Brockman and Mark Haiman, Nilpotent orbit varieties and the atomic decomposition of the \?-Kostka polynomials, Canad. J. Math. 50 (1998), no. 3, 525 -- 537.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quiver varieties; ADHM moduli; equivariant \(K\)-theory; quantum equivariant \(K\)-theory; Macdonald symmetric polynomials
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials torsors; fundamental groups; Grothendieck topologies
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials principal hook lengths; Durfee size; skew characters; symmetric group; skew Schur functions; Schubert Calculus Gutschwager, C.: On principal hook length partitions and durfee sizes in skew characters. Annals Comb. (to appear). arXiv:0802.0417v2
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials permutation; generating function; descent class; diagram; odd length; Schubert variety
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grassmannians; flag manifolds; Schubert cells; Schubert stratification; flattening; equivalence; singularities; bifurcation; Weierstrass points; algebraic curves DOI: 10.1070/RM1991v046n05ABEH002844
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials symplectic manifold; complex surface; Seiberg-Witten invariant; Kodaira double-fibration C LeBrun, Diffeomorphisms, symplectic forms and Kodaira fibrations, Geom. Topol. 4 (2000) 451
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials reflex field; CM curves; Igusa class polynomials Bouyer, F., Streng, M.: Examples of CM curves of genus two defined over the reflex field. LMS J. Comput. Math. (to appear). arXiv:1307.0486
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Hilbert polynomials; moduli space of semi-stable rank 2 vector; Hecke correspondence A. Bertram and A. Szenes, ''Hilbert polynomials of moduli spaces of rank-\(2\). Vector bundles. II,'' Topology, vol. 32, iss. 3, pp. 599-609, 1993.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials \(\ell\)-adic cohomology; Grothendieck topologies; \(\mathfrak p\)-adic fields Hélène Esnault, Coniveau over \?-adic fields and points over finite fields, C. R. Math. Acad. Sci. Paris 345 (2007), no. 2, 73 -- 76 (English, with English and French summaries).
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials symmetric functions; \(k\)-Schur functions; affine Schubert calculus; dual graded graphs; affine nilCoxeter algebra; \(k\)-cores Berg, Chris; Saliola, Franco; Serrano, Luis, The down operator and expansions of near rectangular \(k\)-Schur functions, J. Combin. Theory Ser. A, 120, 3, 623-636, (2013)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials APN functions; finite fields; absolute irreducible polynomials
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials root of orbifold line bundles; polynomiality; double ramification cycle; absolute/relative orbifold Gromov-Witten theory
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Betti numbers; descent systems; H-polynomials; rationally smooth
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials conformal geometric algebra; Darboux Dupin cyclide; quadric surface; double conformal/Darboux cyclide geometric algebra; Clifford geometric algebra Easter, R.B., Hitzer, E.: \textit{Double conformal space-time algebra}, AIP Conference Proceedings, vol. 1798, AIP Publishing, p. 020066 (2017)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Néron symbol; Picard functor; Néron model; duality; Grothendieck pairing Pépin, C., Néron's pairing and relative algebraic equivalence, Algebra Number Theory, 6, 1315-1348, (2012)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quasianalytic perturbation; hyperbolic polynomials; quasianalytic and arc-quasianalytic functions; polynomially bounded structures; eigenvalues; eigenspaces; symmetric and antisymmetric matrices; spectral theorem; quasianalytic diagonalization Krzysztof Jan Nowak, Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices, Ann. Polon. Math. 101 (2011), no. 3, 275 -- 291.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials flag manifolds; nilpotent element; standard tableaux; Young diagram; Schubert cell; hook type; irreducible components Pagnon, NGJ, On the spaltenstein correspondence, Indag. Mathem., 15, 101-114, (2004)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials simple integrable modules; double affine Hecke algebras; perverse sheaves; linear algebraic groups; Lie algebras; Cartan subalgebras; Borel subalgebras; root systems; affine Weyl groups; simple reflections; pairings; equivariant \(K\)-theory; Jordan-Hölder multiplicities of induced modules Vasserot, Eric, Induced and simple modules of double affine Hecke algebras, Duke Math. J., 126, 2, 251-323, (2005)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials ruled surface; double cover; Brauer group Creutz, B., Viray, B.: On Brauer groups of double covers of ruled surfaces. Math. Ann. (2014). 10.1007/s00208-014-1153-0
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials anabelian geometry; Grothendieck conjecture; moduli space; hyperbolic curve; configuration space
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties; cohomology of line bundles; semisimple algebraic groups; Frobenius splitting Lauritzen, N.; Thomsen, J. F., Line bundles on Bott-Samelson varieties, J. Algebraic Geom., 13, 461-473, (2004)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials instructional exposition; textbooks; group theory; field theory and polynomials; commutative rings and algebras; noncommutative rings; algebraic geometry; homological algebra Ash, R. B., Basic abstract algebra. for graduate students and advanced undergraduates, (2007), Dover Publications, Inc. Mineola, NY
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Brauer groups; Picard groups; idempotent kernel endofunctors; Grothendieck category; restriction; extension; compatibility; torsion theories
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials birational structure of double covers of the projective plane Yoshihara, H.: Double coverings of P2. Proc. Japan Acad.66, 233--236 (1990)
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials bibliography; Hilbert's basis theorem; dictionary: commutative algebra-projective algebraic geometry; Hilbert's syzygy theorem; Hilbert's Nullstellensatz; Hilbert polynomials; dimension theory; Dedekind domains; Hilbert-Samuel functions; elimination theory; computer algebra; modules of differentials; homological methods; Koszul complex; Cohen-Macaulay property; duality theory; linkage Eisenbud D, \textit{Commutative Algebra: With a View Toward Algebraic Geometry}, 150, Springer New York, 1995.
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Bibliography; \(L_ 2\)-cohomology; \(\mathbb{D}\)-modules; Beilinson cohomology; regulator maps; Grothendieck motives; degeneration of Hodge structures; intersection homology; Riemann-Hilbert correspondence; Deligne cohomology; variation of mixed Hodge structure; Higgs bundles Brylinski, J.-L., Zucker, S.: An overview of recent advances in Hodge theory. In: Several Complex Variables VI. Encyclopedia Math. Sci., vol. 69, pp. 39--142. Springer, Berlin (1990)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials heights; equidistribution; iteration of polynomials 10.2140/ant.2017.11.1437
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials module of differentials of a curve; group of automorphisms; Grothendieck group; ramification module Kani, Ernst, The {G}alois-module structure of the space of holomorphic differentials of a curve, Journal für die Reine und Angewandte Mathematik. [Crelle's Journal], 367, 187-206, (1986)
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials rational double point; sheaf of logarithmic derivations
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quantum cohomology; flag manifold; Schubert polynomial; elementary symmetric polynomial; standard elementary monomial
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties; Grassmann varieties; spherical varieties
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double-base number system; scalar multiplication; elliptic curve cryptography Doche, C., Habsieger, L.: A tree-based approach for computing double-base chains. In: Mu, Y., Susilo, W., Seberry, J. (eds.) ACISP 2008. LNCS, vol.~5107, pp. 433--446. Springer, Heidelberg (2008)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials zero dimensional systems; Chebyshev curves; Lissajous curves; Lissajous knots; polynomial knots; Chebyshev polynomials; minimal polynomial; Chebyshev forms
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Picard variety; Néron model; Grothendieck's pairing
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert calculus; Wronski map; orthogonal Grassmannian; symmetric tableaux Purbhoo, K., The Wronski map and shifted tableau theory, Int. math. res. not. IMRN, 24, 5706-5719, (2011)
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double field theory; sigma model; dilogarithms Aldi, M., Heluani, R.: Dilogarithms, OPE and twisted T-duality. Int. Math. Res. Not. IMRN \textbf{6}, 1528-1575 (2014). arXiv:1105.4280 [math-ph]
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials motivic Milnor fibre at infinity; Newton polygons; bifurcation values of polynomials; motivic nearby cycles at infinity
| 0
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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Coxeter groups; affine Weyl groups; \(p\)-adic groups; conjugacy classes; class polynomials; admissible sets; Shimura varieties; Deligne-Lusztig varieties; Iwahori subgroup; parahoric subgroup; affine Hecke algebras; cocenters; character tables He, X., Hecke algebras and \textit{p}-adic groups, (), 73-135
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