The absolute order on the hyperoctahedral group
نویسنده
چکیده
The absolute order on the hyperoctahedral group Bn is investigated. Using a poset fiber theorem, it is proved that the order ideal of this poset generated by the Coxeter elements is homotopy Cohen–Macaulay. This method results in a new proof of Cohen–Macaulayness of the absolute order on the symmetric group. Moreover, it is shown that every closed interval in the absolute order on Bn is shellable and an example of a non-Cohen–Macaulay interval in the absolute order on D4 is given. Finally, the closed intervals in the absolute order on Bn and Dn which are lattices are characterized and some of their important enumerative invariants are computed.
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