Séminaire Lotharingien de Combinatoire, 82B.29 (2019), 12 pp.

Eric Marberg and Brendan Pawlowski

Stanley symmetric functions for signed involutions

Abstract. Involution words are variations of reduced words associated to twisted involutions in Coxeter groups. These words are saturated chains in a partial order first considered by Richardson and Springer in their study of symmetric varieties. In the symmetric group, involution words can be enumerated in terms of tableaux using appropriate analogues of the symmetric functions introduced by Stanley to count reduced words. We adapt this approach to the group of signed permutations. We show that the involution words for the longest element in the Coxeter group Cn are in bijection with reduced words for the longest element in An = Sn+1, which are known to be in bijection with standard tableaux of shape (n, n-1, ..., 2, 1).

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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