Broken circuit complexes and hyperplane arrangements
نویسندگان
چکیده
منابع مشابه
Broken Circuit Complexes: Factorizations and Generalizations
Motivated by the question of when the characteristic polynomial of a matroid factorizes, we study join-factorizations of broken circuit complexes and rooted complexes (a more general class of complexes). Such factorizations of complexes induce factorizations not only of the characteristic polynomial but also of the Orlik-Solomon algebra of the matroid. The broken circuit complex of a matroid fa...
متن کاملBroken circuit complexes: Factorizations and generalizations
Motivated by the question of when the characteristic polynomial of a matroid factorizes, we study join-factorizations of broken circuit complexes and rooted complexes (a more general class of complexes). Such factorizations of complexes induce factorizations not only of characteristic polynomial but also of the Orlik-Solomon algebra of the matroid. The broken circuit complex of a matroid factor...
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Let F be a field and let G be a finite graph with a total ordering on its edge set. Richard Stanley noted that the Stanley-Reisner ring F (G) of the broken circuit complex of G is CohenMacaulay. Jason Brown gave an explicit description of a homogeneous system of parameters for F (G) in terms of fundamental cocircuits in G. So F (G) modulo this hsop is a finite dimensional vector space. We conje...
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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...
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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: Journal of Algebraic Combinatorics
سال: 2013
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-013-0435-z