Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement [PDF]
, 2018 This paper studies Markov chains on the chambers of real hyperplane arrangements, a model that generalizes famous examples, such as the Tsetlin library and riffle shuffles.
Nestoridi, Evita
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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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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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Eigenvectors for a random walk on a hyperplane arrangement [PDF]
, 2012 We find explicit eigenvectors for the transition matrix of the Bidigare–Hanlon–Rockmore random walk, from Bidigare et al. (1999) [1]. This is accomplished by using Brown and Diaconisʼ (1998) analysis in [3] of the stationary distribution, together with ...
Graham Denham, Denham, Graham
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Functions of random walks on hyperplane arrangements [PDF]
, 2010 Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes.
Diaconis, Persi +3 more
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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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Lattice Point Counts for the Shi Arrangement and other affinographic hyperplane arrangements [PDF]
, 2006 Hyperplanes of the form xj = xi + c are called affinographic. For an affinographic hyperplane arrangement in R n, such as the Shi arrangement, we study the function f(m) that counts integral points in [1, m] n that do not lie in any hyperplane of the ...
Forge, David +3 more
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Cohomology of $\mathbb{Z}$-local systems on complex hyperplane arrangement complements [PDF]
, 2023 We prove a Cohen-Dimca-Orlik type theorem for rank one $\mathbb{Z}$-local systems on complex hyperplane arrangement complements. This settles a recent conjecture of S.
Wang, Botong +2 more
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Lefschetz properties and hyperplane arrangements [PDF]
Journal of Algebra, 2020 To appear in the Journal of ...
Elisa Palezzato, Michele Torielli
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On the two variable distance enumerator of the Shi hyperplane arrangement [PDF]
, 2008 We give an interpretation for the coefficients of the two variable refinement DSn(q,t) of the distance enumerator of the Shi hyperplane arrangement Sn in n dimensions. This two variable refinement was defined by Stanley in [R.P.
Sivasubramanian, Sivaramakrishnan
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