The absolute order on the hyperoctahedral group

Authors:
Myrto Kallipoliti
Affiliations:
Department of Mathematics, University of Athens, Athens, Greece 15784
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2011

Citing 4
Cited 1

Topological methods

Handbook of combinatorics (vol. 2)
Non-crossing partitions for classical reflection groups

Discrete Mathematics
Note: The absolute order on the symmetric group, constructible partially ordered sets and Cohen--Macaulay complexes

Journal of Combinatorial Theory Series A
Enumerative Combinatorics: Volume 1

Enumerative Combinatorics: Volume 1

The absolute order of a permutation representation of a Coxeter group

Journal of Algebraic Combinatorics: An International Journal

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Abstract

The absolute order on the hyperoctahedral group B n 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 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.