منابع مشابه
Affine and Toric Hyperplane Arrangements
We extend the Billera–Ehrenborg–Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky’s fundamental results on the number of regions.
متن کاملAffine and toric arrangements
We extend the Billera–Ehrenborg–Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For toric arrangements, we also generalize Zaslavsky’s fundamental results on the number of regions. Résumé. Nous étendons l’opérateur de Billera–Ehrenborg–Readdy entre la trellis d’intersection et la trellis de faces d’un ...
متن کاملMatroid Shellability , β - Systems and Affine Hyperplane Arrangements
The broken circuit complex plays a fundamental role for the shellability and homology of matroids, geometric lattices and linear hyperplane arrangements. Here we introduce and study the β-system of a matroid, βnbc(M), whose cardinality is Crapo’s β-invariant. In studying the shellability and homology of base-pointed matroids, geometric semilattices and affine hyperplane arrangements, we find th...
متن کاملRandom Walk and Hyperplane Arrangements
Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuuing schemes used in computer science, biology, and card games. It also includes random walks on zonotopes and zonotopal tilings. We nd the stationary distributions of these Markov chains, give good bounds on the rate of convergence to...
متن کاملBranched Polymers and Hyperplane Arrangements
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 [BI], and Kenyon and Winkler [KW] to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is expressed through the value of the chara...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2009
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-009-9134-x