Geodesic
Hultman elements for the hyperoctahedral groups
Alexander Woo1
1University of Idaho
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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Hultman, Linusson, Shareshian, and Sjöstrand gave a pattern avoidance characterization of the permutations for which the number of chambers of its associated inversion arrangement is the same as the size of its lower interval in Bruhat order. Hultman later gave a characterization, valid for an arbitrary finite reflection group, in terms of distances in the Bruhat graph. On the other hand, the pattern avoidance criterion for permutations had earlier appeared in independent work of Sjöstrand and of Gasharov and Reiner. We give characterizations of the elements of the hyperoctahedral groups satisfying Hultman's criterion that is in the spirit of those of Sjöstrand and of Gasharov and Reiner. We also give a pattern avoidance criterion using the notion of pattern avoidance defined by Billey and Postnikov.
DOI : 10.37236/7636
Classification : 20F55, 05E16
Mots-clés : inversion arrangement, Bruhat order, pattern avoidance, hyperoctahedral groups

Alexander Woo  1

1 University of Idaho 
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Alexander Woo. Hultman elements for the hyperoctahedral groups. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7636

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