Lexicographic shellability for balanced complexes
| dc.creator | Hersh, Patricia | |
| dc.date | 2003-11-16 | |
| dc.date.accessioned | 2026-07-07T05:02:57Z | |
| dc.date.available | 2026-07-07T05:02:57Z | |
| dc.description | We introduce a notion of lexicographic shellability for pure, balanced boolean cell complexes, modelled after the $CL$-shellability criterion of Björner and Wachs for posets and its generalization by Kozlov called $CC$-shellability. We give a lexicographic shelling for the quotient of the order complex of a Boolean algebra of rank $2n$ by the action of the wreath product $S_2\wr S_n$ of symmetric groups, and we provide a partitioning for the quotient complex $Δ(Π_n)/S_n $. Stanley asked for a description of the symmetric group representation $β_S $ on the homology of the rank-selected partition lattice $Π_n^S $ in [St2], and in particular he asked when the multiplicity $b_S(n)$ of the trivial representation in $β_S$ is 0. One consequence of the partitioning for $\dps $ is a (fairly complicated) combinatorial interpretation for $b_S(n) $; another is a simple proof of Hanlon's result that $b_{1,..., i}(n)=0$. Using a result of Garsia and Stanton, we deduce from our shelling for $Δ(B_{2n})/S_2 \wr S_n$ that the ring of invariants $k[x_1,..., x_{2n}]^{S_2\wr S_n}$ is Cohen-Macaulay over any field $k$. | |
| dc.description | 28 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/math/0311262 | |
| dc.identifier | http://arxiv.org/abs/math/0311262 | |
| dc.identifier | J. Algebraic Combinatorics, 17 (2003), no. 1, 27-52 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69214 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E25, 05A18 | |
| dc.title | Lexicographic shellability for balanced complexes | |
| dc.type | text |