Results 1 to 10 of about 12,587 (151)
Order recognition by Schubert polynomials generated by optical near-field statistics via nanometre-scale photochromism [PDF]
Scientific Reports, 2022 Irregular spatial distribution of photon transmission through a photochromic crystal photoisomerized by a local optical near-field excitation was previously reported, which manifested complex branching processes via the interplay of material deformation ...
Kazuharu Uchiyama +8 more
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A Primal-Dual Formulation for Certifiable Computations in Schubert Calculus [PDF]
Foundations of Computational Mathematics, 2015 Formulating a Schubert problem as the solutions to a system of equations in either Pl\"ucker space or in the local coordinates of a Schubert cell typically involves more equations than variables. We present a novel primal-dual formulation of any Schubert
Jonathan D Hauenstein +2 more
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Combinatorial description of the cohomology of the affine flag variety [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigatethe combinatorics of affine Schubert calculus for typeA. We introduce Murnaghan-Nakayama elements and Dunklelements in the affine FK algebra.
Seung Jin Lee
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Discrete Mathematics & Theoretical Computer Science, 2020 In this work triangular puzzles that are composed of unit triangles with labelled edges are considered. To be more precise, the labelled unit triangles that we allow are on the one hand the puzzle pieces that compute Schubert calculus and on the other ...
Sabine Beil
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Genomic Tableaux and Combinatorial $K$-Theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We introduce genomic tableaux, with applications to Schubert calculus. We report a combinatorial rule for structure coefficients in the torus-equivariant $K$-theory of Grassmannians for the basis of Schubert structure sheaves.
Oliver Pechenik, Alexander Yong
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On Schubert calculus in elliptic cohomology [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points.
Cristian Lenart, Kirill Zainoulline
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An equivariant rim hook rule for quantum cohomology of Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis.
Elizabeth Beazley +2 more
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Root-theoretic Young Diagrams, Schubert Calculus and Adjoint Varieties [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Root-theoretic Young diagrams are a conceptual framework to discuss existence of a root-system uniform and manifestly non-negative combinatorial rule for Schubert calculus.
Dominic Searles, Alexander Yong
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Flag Gromov-Witten invariants via crystals [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We apply ideas from crystal theory to affine Schubert calculus and flag Gromov-Witten invariants. By defining operators on certain decompositions of elements in the type-$A$ affine Weyl group, we produce a crystal reflecting the internal structure of ...
Jennifer Morse, Anne Schilling
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Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We use the modules introduced by Kraśkiewicz and Pragacz (1987, 2004) to show some positivity propertiesof Schubert polynomials. We give a new proof to the classical fact that the product of two Schubert polynomialsis Schubert-positive, and also show a ...
Masaki Watanabe
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