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Geometrically constructed bases for homology of partition lattices of types A, B and D
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-7497-2764
2004 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 11, no 2Article in journal (Refereed) Published
Abstract [en]

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 R-d. Let R-1,..., R-k be the bounded regions of a generic hyperplane section of A. We show that there are induced polytopal cycles rho(Ri) in the homology of the proper part LA of the intersection lattice such that {rho(Ri)}(i=1,...,k) is a basis for (H) over tilde (d-2)((L) over bar (A)). 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.

Place, publisher, year, edition, pages
2004. Vol. 11, no 2
Keyword [en]
free lie-algebra, dowling lattices, arrangements, posets
Identifiers
URN: urn:nbn:se:kth:diva-23474ISI: 000221826200003Scopus ID: 2-s2.0-3042675809OAI: oai:DiVA.org:kth-23474DiVA: diva2:342172
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Björner, Anders.

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