Results 21 to 30 of about 1,716 (199)
Cell Complexities in Hyperplane Arrangements [PDF]
Discrete and Computational Geometry, 2004 The complexity of some cells of an hyperplane arrangement in \(R^d\) is the total number of faces of all dimensions of these cells. The authors show that the complexity of \(m\) distinct cells in an arrangement of \(n\) hyperplanes in dimension \(d\geq 4\) is \(O(m^{1/2}n^{d/2}\log^{(\lfloor d/2\rfloor-2)}n)\).
Boris Aronov, Micha Sharir
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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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Branched Polymers and Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2013 We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie, and Kenyon and Winkler to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is ...
Postnikov, Alexander, Meszaros, Karola
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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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Hyperplane Arrangements over the Ring of Integers Modulo N.
, 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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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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Face monoid actions and tropical hyperplane arrangements [PDF]
, 2017 We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin in ...
Kambites, Mark +3 more
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Arrangements of oriented hyperplanes [PDF]
Discrete & Computational Geometry, 1993 The paper refers to arrangements of \(n\) oriented hyperplanes in \(E^ d\). For \(n\) and \(d\) given, the author derives an upper bound on the number \(c_ k\) of convex cells which are covered by precisley \(k\) half-spaces. Denoting the corresponding maximal number by \(C_ k(n,d)\), for \(n>d\) the following recursive inequality holds: \[ C_ k(n,d ...
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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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An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs,
Takuro Abe, Koji Nuida, Yasuhide Numata
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