Hultman elements for the hyperoctahedral groups (Q1640215)

Summary: \textit{A. Hultman} et al. [J. Comb. Theory, Ser. A 116, No. 3, 564--580 (2009; Zbl 1207.05006)] 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. \textit{A. Hultman} [J. Comb. Theory, Ser. A 118, No. 7, 1897--1906 (2011; Zbl 1236.05204)] 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 \textit{J. Sjöstrand} [J. Comb. Theory, Ser. A 114, No. 7, 1182--1198 (2007; Zbl 1124.05006)] and of \textit{V. Gasharov} and \textit{V. Reiner} [J. Lond. Math. Soc., II. Ser. 66, No. 3, 550--562 (2002; Zbl 1064.14056)]. We give characterizations of the elements of the hyperoctahedral groups satisfying Hultman's criterion that is in the spirit of those of Sjöstrand [loc. cit.] and of Gasharov and Reiner [loc. cit.]. We also give a pattern avoidance criterion using the notion of pattern avoidance defined by \textit{S. Billey} and \textit{A. Postnikov} [Adv. Appl. Math. 34, No. 3, 447--466 (2005; Zbl 1072.14065)].