We study the partial orders induced on Wachs and signed Wachs permutations by the Bruhat and weak orders of the symmetric and hyperoctahedral groups. We show that these orders are graded, determine their rank function, characterize their ordering and covering relations, and compute their characteristic polynomials, when partially ordered by Bruhat order, and determine their structure explicitly when partially ordered by right weak order. (c) 2023 Elsevier Ltd. All rights reserved.
Brenti, F., Sentinelli, P. (2024). Wachs permutations, Bruhat order and weak order. EUROPEAN JOURNAL OF COMBINATORICS, 119 [10.1016/j.ejc.2023.103804].
Wachs permutations, Bruhat order and weak order
Brenti, Francesco
;Sentinelli, Paolo
2024-01-01
Abstract
We study the partial orders induced on Wachs and signed Wachs permutations by the Bruhat and weak orders of the symmetric and hyperoctahedral groups. We show that these orders are graded, determine their rank function, characterize their ordering and covering relations, and compute their characteristic polynomials, when partially ordered by Bruhat order, and determine their structure explicitly when partially ordered by right weak order. (c) 2023 Elsevier Ltd. All rights reserved.| File | Dimensione | Formato | |
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