%0 Journal Article
%T The absolute order on the hyperoctahedral group
%A Myrto Kallipoliti
%J Mathematics
%D 2010
%I arXiv
%X The absolute order on the hyperoctahedral group $B_n$ 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 $B_n$ is shellable and an example of a non-Cohen-Macaulay interval in the absolute order on $D_4$ is given. Finally, the closed intervals in the absolute order on $B_n$ and $D_n$ which are lattices are characterized and some of their important enumerative invariants are computed.
%U http://arxiv.org/abs/1002.0440v2