Results 1 to 10 of about 10,484 (179)
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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Skew Divided Difference Operators and Schubert Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group.
Anatol N. Kirillov
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Schubert Polynomials and Quiver Formulas [PDF]
Duke Mathematical Journal, 2002 The work of Buch and Fulton established a formula for a general kind of degeneracy locus associated to an oriented quiver of type $A$. The main ingredients in this formula are Schur determinants and certain integers, the quiver coefficients, which ...
Buch, Anders Skovsted +3 more
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Schubert polynomial expansions revisited
Forum of Mathematics, SigmaWe give an elementary approach utilizing only the divided difference formalism for obtaining expansions of Schubert polynomials that are manifestly nonnegative, by studying solutions to the equation $\sum Y_i\partial _i=\operatorname {id}$ on ...
Philippe Nadeau +2 more
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Upper bounds of Schubert polynomials [PDF]
Science China Mathematics, 2021 14 pages, 4 ...
Fan, Neil Jiuyu, Guo, Peter Long
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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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The Prism tableau model for Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1; x2; : : :]. We suggest the prism tableau model for these polynomials.
Anna Weigandt, Alexander Yong
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A dual approach to structure constants for K-theory of Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The problem of computing products of Schubert classes in the cohomology ring can be formulated as theproblem of expanding skew Schur polynomial into the basis of ordinary Schur polynomials. We reformulate theproblem of computing the structure constants
Huilan Li, Jennifer Morse, Pat Shields
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Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 In their 1987 paper Kraskiewicz and Pragacz defined certain modules, which we call KP modules, over the upper triangular Lie algebra whose characters are Schubert polynomials.
Masaki Watanabe
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Double Schubert polynomials for the classical Lie groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 For each infinite series of the classical Lie groups of type $B$, $C$ or $D$, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank.
Takeshi Ikeda +2 more
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