Results 41 to 50 of about 1,232 (194)
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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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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Bigraphical arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson.
Sam Hopkins, David Perkinson
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Cutting hyperplane arrangements [PDF]
Proceedings of the sixth annual symposium on Computational geometry - SCG '90, 1990 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Equivariant perverse sheaves on Coxeter arrangements and buildings [PDF]
Épijournal de Géométrie Algébrique, 2019 When $W$ is a finite Coxeter group acting by its reflection representation on $E$, we describe the category ${\mathsf{Perv}}_W(E_{\mathbb C}, {\mathcal{H}}_{\mathbb C})$ of $W$-equivariant perverse sheaves on $E_{\mathbb C}$, smooth with respect to the ...
Martin H. Weissman
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Free hyperplane arrangements over arbitrary fields [PDF]
, 2020 In this paper, we study the class of free hyperplane arrangements. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness over ...
Torielli, Michele, Palezzato, Elisa
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On the freeness of hypersurface arrangements consisting of hyperplanes and spheres
Open Mathematics, 2018 Let V be a smooth variety. A hypersurface arrangement 𝓜 in V is a union of smooth hypersurfaces, which locally looks like a union of hyperplanes. We say 𝓜 is free if all these local models can be chosen to be free hyperplane arrangements.
Gao Ruimei, Dai Qun, Li Zhe
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Graded Linearity of Stanley–Reisner Ring of Broken Circuit Complexes
Journal of Mathematics, 2022 This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring A=kx1,…,xn.
Mohammad Reza-Rahmati, Gerardo Flores
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Projection Volumes of Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2011 We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones is given by the coefficients of the characteristic polynomial of the arrangement. This settles the conjecture of Drton and Klivans that this held for all finite real reflection arrangements. The methods used are geometric and combinatorial. As a
Caroline J. Klivans, Ed Swartz
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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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