Change search
ReferencesLink to record
Permanent link

Direct link
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KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-7497-2764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 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
URN: urn:nbn:se:kth:diva-23474ISI: 000221826200003ScopusID: 2-s2.0-3042675809OAI: diva2:342172
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

Open Access in DiVA

No full text


Search in DiVA

By author/editor
Björner, Anders.
By organisation
In the same journal
The Electronic Journal of Combinatorics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 14 hits
ReferencesLink to record
Permanent link

Direct link