Results 1 to 10 of about 257 (124)
Affine Bruhat order and Demazure products
Forum of Mathematics, SigmaWe give new descriptions of the Bruhat order and Demazure products of affine Weyl groups in terms of the weight function of the quantum Bruhat graph.
Felix Schremmer
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Bruhat interval polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Let $u$ and $v$ be permutations on $n$ letters, with $u$ ≤ $v$ in Bruhat order. A Bruhat interval polytope $Q_{u,v}$ is the convex hull of all permutation vectors $z=(z(1),z(2),...,z(n))$ with $u$ ≤ $z$ ≤ $v$.
Emmanuel Tsukerman, Lauren Williams
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Intervals and factors in the Bruhat order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Combinatorics
Bridget Eileen Tenner
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Maximal Newton polygons via the quantum Bruhat graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 This paper discusses a surprising relationship between the quantum cohomology of the variety of complete flags and the partially ordered set of Newton polygons associated to an element in the affine Weyl group.
Elizabeth T. Beazley
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Monomial Nonnegativity and the Bruhat Order [PDF]
The Electronic Journal of Combinatorics, 2005 We show that five nonnegativity properties of polynomials coincide when restricted to polynomials of the form $x_{1,\pi(1)}\cdots x_{n,\pi(n)} - x_{1,\sigma(1)}\cdots x_{n,\sigma(n)}$, where $\pi$ and $\sigma$ are permutations in $S_n$. In particular, we show that each of these properties may be used to characterize the Bruhat order on $S_n$.
Drake, Brian +2 more
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A uniform model for Kirillov―Reshetikhin crystals [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We present a uniform construction of tensor products of one-column Kirillov–Reshetikhin (KR) crystals in all untwisted affine types, which uses a generalization of the Lakshmibai–Seshadri paths (in the theory of the Littelmann path model).
Cristian Lenart +4 more
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On the little secondary Bruhat order
The Electronic Journal of Linear Algebra, 2021 Let $R$ and $S$ be two sequences of positive integers in nonincreasing order having the same sum. We denote by ${\cal A}(R,S)$ the class of all $(0,1)$-matrices having row sum vector $R$ and column sum vector $S$. Brualdi and Deaett (More on the Bruhat order for $(0,1)$-matrices, Linear Algebra Appl., 421:219--232, 2007) suggested the study of the ...
Rosário Fernandes +2 more
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The Sorting Order on a Coxeter Group [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Let $(W,S)$ be an arbitrary Coxeter system. For each sequence $\omega =(\omega_1,\omega_2,\ldots) \in S^{\ast}$ in the generators we define a partial order― called the $\omega \mathsf{-sorting order}$ ―on the set of group elements $W_{\omega} \subseteq W$
Drew Armstrong
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Generalized Dyck tilings (Extended Abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas for forests and the combinatorics of Hermite polynomials. The first goal of
Matthieu Josuat-Vergès, Jang Soo Kim
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Moment graphs and KL-polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Motivated by a result of Fiebig (2007), we categorify some properties of Kazhdan-Lusztig polynomials via sheaves on Bruhat moment graphs. In order to do this, we develop new techniques and apply them to the combinatorial data encoded in these moment ...
Martina Lanini
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