A Basis for the Top Homology of a Generalized Partition Lattice
dc.contributor.author | Kerr, Julie | en_US |
dc.date.accessioned | 2006-09-11T17:37:10Z | |
dc.date.available | 2006-09-11T17:37:10Z | |
dc.date.issued | 1999-01 | en_US |
dc.identifier.citation | Kerr, Julie; (1999). "A Basis for the Top Homology of a Generalized Partition Lattice." Journal of Algebraic Combinatorics 9(1): 47-60. <http://hdl.handle.net/2027.42/46306> | en_US |
dc.identifier.issn | 0925-9899 | en_US |
dc.identifier.issn | 1572-9192 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/46306 | |
dc.description.abstract | For a fixed positive integer k, consider the collection of all affine hyperplanes in n-space given by xi − xj = m, where i, j ∈ [n], i ≠ j, and m ∈ {0, 1,..., k}. Let Ln,k be the set of all nonempty affine subspaces (including the empty space) which can be obtained by intersecting some subset of these affine hyperplanes. Now give Ln,k a lattice structure by ordering its elements by reverse inclusion. The symmetric group Gn acts naturally on Ln,k by permuting the coordinates of the space, and this action extends to an action on the top homology of Ln,k. It is easy to show by computing the character of this action that the top homology is isomorphic as an Gn-module to a direct sum of copies of the regular representation, CGn. In this paper, we construct an explicit basis for the top homology of Ln,k, where the basis elements are indexed by all labelled, rooted, (k + 1)-ary trees on n-vertices in which the root has no 0-child. This construction gives an explicit Gn-equivariant isomorphism between the top homology of Ln,k and a direct sum of copies of CGn. | en_US |
dc.format.extent | 116243 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers; Springer Science+Business Media | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Computer Science, General | en_US |
dc.subject.other | Group Theory and Generalizations | en_US |
dc.subject.other | Order, Lattices, Ordered Algebraic Structures | en_US |
dc.subject.other | Combinatorics | en_US |
dc.subject.other | Convex and Discrete Geometry | en_US |
dc.subject.other | Intersection Lattice | en_US |
dc.subject.other | Partition Lattice | en_US |
dc.subject.other | Homology | en_US |
dc.subject.other | Regular Representation | en_US |
dc.subject.other | Rooted Tree | en_US |
dc.title | A Basis for the Top Homology of a Generalized Partition Lattice | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1109 | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/46306/1/10801_2004_Article_187203.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1023/A:1018663030935 | en_US |
dc.identifier.source | Journal of Algebraic Combinatorics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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