The absolute order on the hyperoctahedral group
Combinatorics
2010-03-26 v2
Abstract
The absolute order on the hyperoctahedral group is investigated. It is proved that the order ideal of this poset generated by the Coxeter elements is homotopy Cohen-Macaulay and the M\"obius number of this ideal is computed. Moreover, it is shown that every closed interval in the absolute order on is shellable and an example of a non-Cohen-Macaulay interval in the absolute order on is given. Finally, the closed intervals in the absolute order on and which are lattices are characterized and some of their important enumerative invariants are computed.
Keywords
Cite
@article{arxiv.1002.0440,
title = {The absolute order on the hyperoctahedral group},
author = {Myrto Kallipoliti},
journal= {arXiv preprint arXiv:1002.0440},
year = {2010}
}
Comments
26 pages, 6 figures. Theorem 1.3 of the previous version of this paper is omitted due to a gap in the proof.