Results 11 to 20 of about 10,484 (179)
Quantum Schubert polynomials [PDF]
Journal of the American Mathematical Society, 1997 {Let \(Fl_n\) be the manifold of complete flags in the \(n\)-dimensional vector space \(\mathbb C^n\). Inspired from ideas from string theory, recently the concept of quantum cohomology ring \(QH^*(X,\mathbb Z)\) of a Kähler algebraic manifold \(X\) has been defined.
Fomin, Sergey +2 more
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Double Schubert polynomials do have saturated Newton polytopes
Forum of Mathematics, Sigma, 2023 We prove that double Schubert polynomials have the saturated Newton polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees.
Federico Castillo +3 more
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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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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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Zero-one Schubert polynomials [PDF]
Mathematische Zeitschrift, 2020 AbstractWe prove that if $$\sigma \in S_m$$ σ ∈ S m is a pattern of $$w \in S_n$$ w ∈
Fink, A, Mészáros, K, St. Dizier, A
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Which Schubert varieties are local complete intersections? [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We characterize by pattern avoidance the Schubert varieties for $\mathrm{GL}_n$ which are local complete intersections (lci). For those Schubert varieties which are local complete intersections, we give an explicit minimal set of equations cutting out ...
Henning Úlfarsson, Alexander Woo
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Schur polynomials and matrix positivity preservers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A classical result by Schoenberg (1942) identifies all real-valued functions that preserve positive semidefi- niteness (psd) when applied entrywise to matrices of arbitrary dimension.
Alexander Belton +3 more
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A Murgnahan-Nakayama rule for Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We expose a rule for multiplying a general Schubert polynomial with a power sum polynomial in $k$ variables. A signed sum over cyclic permutations replaces the signed sum over rim hooks in the classical Murgnahan-Nakayama rule. In the intersection theory
Andrew Morrison
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RC-Graphs and Schubert Polynomials [PDF]
Experimental Mathematics, 1993 Using a formula of Billey, Jockusch and Stanley, Fomin and Kirillov have introduced a new set of diagrams that encode the Schubert polynomials. We call these objects rc-graphs. We define and prove two variants of an algorithm for constructing the set of all rc-graphs for a given permutation.
Bergeron, Nantel, Billey, Sara
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Product of Stanley symmetric functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We study the problem of expanding the product of two Stanley symmetric functions $F_w·F_u$ into Stanley symmetric functions in some natural way. Our approach is to consider a Stanley symmetric function as a stabilized Schubert polynomial $F_w=\lim _n ...
Nan Li
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