The absolute order on the hyperoctahedral group
Kallipoliti, Myrto
الأصل · EN
The absolute order on the hyperoctahedral group Bₙ is investigated. It is proved that the order ideal of this poset generated by the Coxeter elements is homotopy Cohen-Macaulay and the Möbius number of this ideal is computed. 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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