Results 11 to 20 of about 351,610 (104)
Hyperplane arrangement face algebras and their associated Markov chains.
, 1997 Let ${\cal A}$ be a hyperplane arrangement and let F and G be two of its faces. We define the product of F and G to be the smallest face whose closure contains F and which is separated from G by the fewest number of hyperplanes. Extending this product to
Bidigare, Thomas Patrick
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Schubert varieties, inversion arrangements, and Peterson translation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We show that an element $\mathcal{w}$ of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement $\mathcal{I} (\mathcal{w})$ associated to the inversion set of \mathcal{w} is inductively free, and the product $(d_1+1) ...(d_l+
William Slofstra
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Hyperplane Arrangements and Diagonal Harmonics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 In 2003, Haglund's bounce statistic gave the first combinatorial interpretation of the q,t-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type
Drew Armstrong
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Hyperplane Arrangements over the Ring of Integers Modulo N. [PDF]
, 2023 Let V be a finite vector space of dimension n over the field K. A hyperplane in V is an n − 1 dimensional subspace of V defined by an equation of the form∑ni=1 aixi = 0, ai ∈ K, (x1, ..., xn) ∈ V .
Obeahon, Ehiareshan James
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Geometric aspects of the Jacobian of a hyperplane arrangement [PDF]
, 2023 An embedding of the complete bipartite graph $K_{3,3}$ in $\mathbb{P}^2$ gives rise to both a line arrangement and a bar-and-joint framework. For a generic placement of the six vertices, the graded Betti numbers of the logarithmic module of derivations ...
Sidman, Jessica +2 more
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The Shi arrangement and the Ish arrangement [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 This paper is about two arrangements of hyperplanes. The first — the Shi arrangement — was introduced by Jian-Yi Shi to describe the Kazhdan-Lusztig cells in the affine Weyl group of type A.
Drew Armstrong, Brendon Rhoades
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The theorem of Lie and hyperplane subalgebras of Lie algebras [PDF]
, 1992 Poguntke D. The theorem of Lie and hyperplane subalgebras of Lie algebras. Geometriae Dedicata.
Poguntke, Detlev
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Poset topology and homological invariants of algebras arising in algebraic combinatorics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics. We explore several applications of this interplay.
Stuart Margolis +2 more
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The module of affine descents [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The goal of this paper is to introduce an algebraic structure on the space spanned by affine descent classes of a Weyl group, by analogy and in relation to the structure carried by ordinary descent classes.
Marcelo Aguiar, Kile T. Petersen
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A computation on the decomposition factors of D -modules over a hyperplane arrangement in space [PDF]
, 2020 Let m be a positive integer,α_i:C^n⟶C^n, for i=1,2,…,m be linear forms and H_i={P∈C^n:α_i (P)=0} be the corresponding hyperplane for each i=1,2,…,m . The linear forms α_1,α_2,…,α_m define a hyperplane arrangement and X=C^n\V(α), where α=∏_(i=1)^m α_i and
Ababaw, Tilahun, Demelash, Smegnsh
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