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Deformations of Coxeter Hyperplane Arrangements
Journal of Combinatorial Theory - Series A, 2000 33 ...
Alexander Postnikov, Richard P Stanley
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Projection Volumes of Hyperplane Arrangements [PDF]
Discrete and 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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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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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 +2 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.
openaire +1 more source
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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Twisted Alexander modules of hyperplane arrangement complements
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021Eva Elduque
exaly
Lattice point counts for the Shi arrangement and other affinographic hyperplane arrangements
Journal of Combinatorial Theory - Series A, 2007David Forge, Thomas Zaslavsky
exaly