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arXiv · 2301.02628

Pinnacle sets of signed permutations

Nicolle González·Pamela E. Harris·Gordon Rojas Kirby·Mariana Smit Vega Garcia·Bridget Eileen Tenner
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Abstract

Pinnacle sets record the values of the local maxima for a given family of permutations. They were introduced by Davis-Nelson-Petersen-Tenner as a dual concept to that of peaks, previously defined by Billey-Burdzy-Sagan. In recent years pinnacles and admissible pinnacles sets for the type $A$ symmetric group have been widely studied. In this article we define the pinnacle set of signed permutations of types $B$ and $D$. We give a closed formula for the number of type $B$/$D$ admissible pinnacle sets and answer several other related enumerative questions.

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Nicolle González, Pamela E. Harris, Gordon Rojas Kirby, Mariana Smit Vega Garcia, Bridget Eileen Tenner. 2023-01-06. Pinnacle sets of signed permutations. https://arxiv.org/abs/2301.02628

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