منابع مشابه
New inequalities for subspace arrangements
For each positive integer n ≥ 4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n = 4 we recover Ingleton’s inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also...
متن کاملDerivation radical subspace arrangements
In this note we study modules of derivations on collections of linear subspaces in a finite dimensional vector space. The central aim is to generalize the notion of freeness from hyperplane arrangements to subspace arrangements. We call this generalization ‘derivation radical’. We classify all coordinate subspace arrangements that are derivation radical and show that certain subspace arrangemen...
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In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When k = 2, these arrangements correspond to the well-studied Coxeter arrangements. Brieskorn (1971) showed that the fundamental group of the complement of the type W Coxeter arrangement (over C) is isomorphic to the pure Artin group of type W . Khovanov (1996) gav...
متن کاملWonderful Models of Subspace Arrangements
0 Introduction In this paper we describe, for any given nite family of sub-spaces of a vector space or for linear subspaces in aane or projective space, a smooth model, proper over the given space, in which the complement of these subspaces is unchanged but the family of subspaces is replaced by a divisor with normal crossings. This model can be described explicitly in a combinatorial way and a...
متن کاملLink complexes of subspace arrangements
Given a simplicial hyperplane arrangement H and a subspace arrangement A embedded in H, we define a simplicial complex ∆A,H as the subdivision of the link of A induced by H. In particular, this generalizes Steingŕımsson’s coloring complex of a graph. We do the following: (1) When A is a hyperplane arrangement, ∆A,H is shown to be shellable. As a special case, we answer affirmatively a question ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2009.10.014