Pinnacle sets of signed permutations
Nicolle Gonz\'alez, Pamela E. Harris, Gordon Rojas Kirby, Mariana Smit, Vega Garcia, Bridget Eileen Tenner

TL;DR
This paper extends the concept of pinnacle sets from permutations to signed permutations of types B and D, providing formulas and enumerative results for admissible pinnacle sets in these groups.
Contribution
It introduces the definition of pinnacle sets for signed permutations of types B and D and derives closed formulas for counting admissible pinnacle sets.
Findings
Closed formula for the number of admissible pinnacle sets in types B and D
Enumeration of pinnacle sets for signed permutations
Extension of pinnacle set theory to signed permutation groups
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 symmetric group have been widely studied. In this article we define the pinnacle set of signed permutations of types and . We give a closed formula for the number of type / admissible pinnacle sets and answer several other related enumerative questions.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Advanced Combinatorial Mathematics
