Myrto Kallipoliti

The absolute order on the hyperoctahedral group
dmtcs:2689 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2009,
DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)

https://doi.org/10.46298/dmtcs.2689
The absolute order on the hyperoctahedral groupArticle
Authors: Myrto Kallipoliti ^{1}
0000000321886552
Myrto Kallipoliti
1 Department of Mathematics [Athens]
The absolute order on the hyperoctahedral group $B_n$ is investigated. It is shown that every closed interval in this order is shellable, those closed intervals which are lattices are characterized and their zeta polynomials are computed. Moreover, using the notion of strong constructibility, it is proved that the order ideal generated by the Coxeter elements of $B_n$ is homotopy CohenMacaulay and the Euler characteristic of the order complex of the proper part of this ideal is computed. Finally, an example of a non CohenMacaulay closed interval in the absolute order on the group $D_4$ is given and the closed intervals of $D_n$ which are lattices are characterized.
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Bibliographic References
5 Documents citing this article
Alexander Woo, 2018, Hultman Elements for the Hyperoctahedral Groups, The Electronic journal of combinatorics/The journal of combinatorics, 25, 2, 10.37236/7636, https://doi.org/10.37236/7636.
Christos A. Athanasiadis;Yuval Roichman, 2013, The absolute order of a permutation representation of a Coxeter group, arXiv (Cornell University), 39, 1, pp. 7598, 10.1007/s1080101304398.
Myrto Kallipoliti;Martina Kubitzke, 2013, A Poset Fiber Theorem for Doubly CohenMacaulay Posets and Its Applications, Annals of combinatorics, 17, 4, pp. 711731, 10.1007/s0002601302038.
Myrto Kallipoliti;Martina Kubitzke, 2011, Double homotopy CohenMacaulayness for the poset of injective words and the classical NCpartition lattice, Discrete mathematics and theoretical computer science/Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO,..., Proceedings, 10.46298/dmtcs.2935, https://doi.org/10.46298/dmtcs.2935.