Geometrically Constructed Bases for Homology of Non-Crossing Partition Lattices

2008/06/25 by Aisling Kenny, Kenny, Aisling
Mathematics · #20F55 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:20F55

paper · pdf · doi:10.48550/arxiv.0806.4151

9 pages, 1 figure Reference added

arxiv created 2008/07/15 · arxiv updated 2009/12/01

Abstract

For any finite, real reflection group W, we construct a geometric basis for the homology of the corresponding non-crossing partition lattice. We relate this to the basis for the homology of the corresponding intersection lattice introduced by Björner and Wachs in \citeBW using a general construction of a generic affine hyperplane for the central hyperplane arrangement defined by W.

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