On Flag Vectors, the Dowling Lattice, and Braid Arrangements
نویسندگان
چکیده
منابع مشابه
On Flag Vectors, the Dowling Lattice, and Braid Arrangements
We study complex hyperplane arrangements whose intersection lattices, known as the Dowling lattices, are a natural generalization of the partition lattice. We give a combinatorial description of the Dowling lattice via enriched partitions to obtain an explicit EL-labeling and then find a recursion for the flag h-vector in terms of weighted derivations. When the hyperplane arrangements are real ...
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We define the Dowling transform of a real frame arrangement and show how the characteristic polynomial changes under this transformation. As a special case, the Dowling transform sends the braid arrangement An to the Dowling arrangement. Using Zaslavsky's characterization of supersolvability of signed graphs, we show supersolvability of an arrangement is preserved under the Dowling transform. W...
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This note defines a flag vector for i-graphs. The construction applies to any finite combinatorial object that can be shelled. Two possible connections to quantum topology are mentioned. Further details appear in the author’s On quantum topology, hypergraphs and flag vectors, (preprint q-alg/9708001). The purpose of this note is to state concisely a new combinatorial concept. This note is an an...
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متن کاملFlag Vectors
This paper deenes for each object X that can be constructed out of a nite number of vertices and cells a vector fX lying in a nite dimensional vector space. This is the ag vector of X. It is hoped that the quantum topological invariants of a manifold M can be expressed as linear functions of the ag vector of the i-graph that arises from any suitable triangulation T of M. Flag vectors are also d...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1999
ISSN: 0179-5376
DOI: 10.1007/pl00009428