On The Homology Of The H,K-Equal Dowling Lattice
SIAM Journal on Discrete Mathematics(2003)
摘要
We define a Dowling lattice generalization of the k-equal partition lattice and the h, k-equal signed partition lattice. We use the theory of lexicographical shellability to show that it has the homotopy type of a wedge of spheres, to describe its Betti numbers, and to give a basis for its homology in terms of labelled trees. For cyclic groups, the h, k-equal Dowling lattice arises as the lattice of intersections of a complex subspace arrangement. We use Whitney homology to compute the cohomology of the complement of this arrangement. Our results generalize and unify previous research.
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关键词
Dowling lattice,lexicographical shellability,poset,homology,subspace arrangement
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