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COMBINATORICS
2004

Geometrically Constructed Bases for Homology of Partition Lattices

8 years 11 months ago
Geometrically Constructed Bases for Homology of Partition Lattices
Abstract. We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types A, B and D. This extends and explains the "splitting basis" for the homology of the partition lattice given in [20], thus answering a question asked by R. Stanley. More explicitly, the following general technique is presented and utilized. Let A be a central and essential hyperplane arrangement in Rd . Let R1, . . . , Rk be the bounded regions of a generic hyperplane section of A. We show that there are induced polytopal cycles Ri in the homology of the proper part LA of the intersection lattice such that {Ri }i=1,...,k is a basis for Hd-2(LA). This geometric method for constructing combinatorial homology bases is applied to the Coxeter arrangements of types A, B and D, and to some interpolating arrangements.
Anders Björner, Michelle L. Wachs
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Where COMBINATORICS
Authors Anders Björner, Michelle L. Wachs
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