Results 21 to 30 of about 10,484 (179)
Specializations of Grothendieck polynomials [PDF]
, 2003 We prove a formula for double Schubert and Grothendieck polynomials specialized to two rearrangements of the same set of variables. Our formula generalizes the usual formulas for Schubert and Grothendieck polynomials in terms of RC-graphs, and it gives ...
Buch, Anders S., Rimanyi, Richard
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Gröbner geometry of Schubert polynomials [PDF]
Annals of Mathematics, 2005 Our main theorems provide a single geometric setting in which polynomial representatives for Schubert classes in the integral cohomology ring of the flag manifold are determined uniquely, and have positive coefficients for geometric reasons. This results in a geometric explanation for the naturality of Schubert polynomials and their associated ...
Knutson, Allen, Miller, Ezra
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Schubert polynomials and $k$-Schur functions (Extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function can be understood from the multiplication in the space of dual $k$-Schur functions. Using earlier work by the second author,
Carolina Benedetti, Nantel Bergeron
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Toric matrix Schubert varieties and root polytopes (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Start with a permutation matrix π and consider all matrices that can be obtained from π by taking downward row operations and rightward column operations; the closure of this set gives the matrix Schubert variety Xπ.
Laura Escobar, Karola Mészáros
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Schubert functors and Schubert polynomials
European Journal of Combinatorics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kraśkiewicz, Witold, Pragacz, Piotr
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Quantum double Schubert polynomials represent Schubert classes [PDF]
Proceedings of the American Mathematical Society, 2013 The quantum double Schubert polynomials studied by Kirillov and Maeno, and by Ciocan-Fontanine and Fulton, are shown to represent Schubert classes in Kim’s presentation of the equivariant quantum cohomology of the flag variety. Parabolic analogues of quantum double Schubert polynomials are introduced and shown to represent Schubert classes in the ...
Lam, Thomas, Shimozono, Mark
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Schubert Polynomials and $k$-Schur Functions [PDF]
The Electronic Journal of Combinatorics, 2014 The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood combinatorially from the multiplication in the space of dual $k$-Schur functions.
Benedetti, Carolina, Bergeron, Nantel
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Deodhar Elements in Kazhdan-Lusztig Theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 The Kazhdan-Lusztig polynomials for finite Weyl groups arise in representation theory as well as the geometry of Schubert varieties. It was proved very soon after their introduction that they have nonnegative integer coefficients, but no simple all ...
Brant Jones
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A Demazure crystal construction for Schubert polynomials [PDF]
, 2017 Stanley symmetric functions are the stable limits of Schubert polynomials. In this paper, we show that, conversely, Schubert polynomials are Demazure truncations of Stanley symmetric functions.
Assaf, Sami, Schilling, Anne
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