Results 161 to 170 of about 1,230 (193)
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Modifications of hyperplane arrangements
Journal of Combinatorial Theory, Series A, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Houshan Fu, Suijie Wang
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New characterizations of freeness for hyperplane arrangements [PDF]
Journal of Algebraic Combinatorics, 2019 In this article, we describe two new characterizations of freeness for hyperplane arrangements via the study of the generic initial ideal and of the sectional matrix of the Jacobian ideal of ...
Anna Maria Bigatti +2 more
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Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids [PDF]
Annals of Combinatorics, 2021 A catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971. These arrangements naturally generalize finite Coxeter arrangements and also the weak order through the poset of regions.
Michael Cuntz +2 more
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Hyperplane arrangements between Shi and Ish [PDF]
Electronic Notes in Discrete Mathematics, 2018 We introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions -- the connected components of the ...
Rui Duarte, Antonio Guedes De Oliveira
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The diffeomorphism type of small hyperplane arrangements is combinatorially determined [PDF]
Advances in Geometry, 2019 It is known that there exist hyperplane arrangements with the same underlying matroid that admit non-homotopy equivalent complement manifolds. Here we show that, in any rank, complex central hyperplane arrangements with up to 7 hyperplanes and the same ...
Matteo Gallet
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On the Zone Theorem for Hyperplane Arrangements
SIAM Journal on Computing, 1993In the last years many interesting papers about problems of computational geometry deal with arrangements of hyperplanes in \(d\)-dimensional real space. The known zone theorem says that the number of faces bounding the cells intersected by another hyperplane is \(O(n^{d-1})\).
Herbert Edelsbrunner +2 more
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, 2017 This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and ...
Dimca, Alexandru.author.authttp://id.loc.gov/vocabulary/relators/aut +1 more
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2003
There are many fields which are similar in spirit and related in the methods used and results obtained to the combinatorial theory of polytopes. The present chapter is devoted to one such field: to questions dealing with arrangements of (or partitions by) hyperplanes.
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There are many fields which are similar in spirit and related in the methods used and results obtained to the combinatorial theory of polytopes. The present chapter is devoted to one such field: to questions dealing with arrangements of (or partitions by) hyperplanes.
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Moduli of Weighted Hyperplane Arrangements
2015Preface.- Introduction.- Stable pairs and their moduli.- Stable toric varieties.- Matroids.- Matroid polytopes and tilings.- Weighted stable hyperplane arrangements.- Abelian Galois covers.- Bibliography.
G. Bini +3 more
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On the zone of a surface in a hyperplane arrangement
2005Let H be a collection of n hyperplanes in ℝ d , let A denote the arrangement of H, and let σ be a (d - 1)-dimensional algebraic surface of low degree, or the boundary of a convex body in ℝd. The zone of σ in A is the collection of cells of A crossed by σ. We show that the total number of faces bounding the cells of the zone of σ is O(nd−1 log n).
Boris Aronov, Micha Sharir
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