Results 31 to 40 of about 294 (153)
Shortest path poset of finite Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We define a poset using the shortest paths in the Bruhat graph of a finite Coxeter group $W$ from the identity to the longest word in $W, w_0$. We show that this poset is the union of Boolean posets of rank absolute length of $w_0$; that is, any shortest
Saúl A. Blanco
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Representations on Hessenberg Varieties and Young's Rule [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We combinatorially construct the complex cohomology (equivariant and ordinary) of a family of algebraic varieties called regular semisimple Hessenberg varieties. This construction is purely in terms of the Bruhat order on the symmetric group. From this a
Nicholas Teff
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Bruhat-Chevalley Order in Reductive Monoids [PDF]
Journal of Algebraic Combinatorics, 2004 Let \(M\) be an irreducible algebraic monoid with zero. \(M\) is a reductive monoid if it is the Zariski closure in \(M_n(K)\) of a reductive group \(G\subseteq\text{GL}_n(K)\). The Bruhat-Chevalley order in \(G\) has a natural extension to \(M\). The Renner monoid \(R\) for \(M\) takes the place of the Weyl group \(W\) for \(G\).
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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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Involutions under Bruhat order and labeled Motzkin paths [PDF]
European Journal of Combinatorics, 2022 In this note, we introduce a statistic on Motzkin paths that describes the rank generating function of Bruhat order for involutions. Our proof relies on a bijection introduced by Philippe Biane from permutations to certain labeled Motzkin paths and a recently introduced interpretation of this rank generating function in terms of visible inversions.
Coopman, Michael, Hamaker, Zachary
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Bending the Bruhat-Tits tree. Part I. Tensor network and emergent Einstein equations
Journal of High Energy Physics, 2021 As an extended companion paper to [1], we elaborate in detail how the tensor network construction of a p-adic CFT encodes geometric information of a dual geometry even as we deform the CFT away from the fixed point by finding a way to assign distances to
Lin Chen, Xirong Liu, Ling-Yan Hung
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Ricci curvature of Bruhat orders
Advances in Applied Mathematics, 2022 We study the Ricci curvature of the Hasse diagrams of the Bruhat order of finite irreducible Coxeter groups. For this purpose we compute the maximum degree of these graphs for types $B_n$ and $D_n$. The proof uses a new graph $Γ(π)$ defined for any element $π$ in the corresponding group.
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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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Chains in the Bruhat order [PDF]
Journal of Algebraic Combinatorics, 2008 36 ...
Postnikov, Alexander +1 more
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Towers of powers and bruhat order
European Journal of Combinatorics, 1992 In this short paper, the authors provide a counterexample ...
Griggs, Jerrold R., Wachs, Michelle L.
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