Further results on pinnacle sets

Minnich, Quinn

doi:10.1016/j.disc.2022.113296

Cited by 2 publications

(2 citation statements)

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“…gave a recursive formula for the number of permutations in S n with a given pinnacle set p(n) and asked whether a more efficient expression could be computed. This paper led to a sequence of articles in recent years, many focused on improved and faster formulas for p(n), by realizing permutations with given pinnacle sets as invariants under certain modified S n -actions [5,9] or via more traditional enumerative methods [8,10,11]. In related work, Rusu [13] and Rusu-Tenner [14] deepened the knowledge of pinnacles in S n by investigating further properties of these statistics and characterizing admissible pinnacle orderings.…”

Section: Introductionmentioning

confidence: 99%

Pinnacle sets of signed permutations

González¹,

Harris²,

Kirby³

et al. 2023

Preprint

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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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Section: Introductionmentioning

confidence: 99%

Pinnacle sets of signed permutations

González¹,

Harris²,

Kirby³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Pinnacle sets of permutations have received great interest since their introduction in [3] by Davis, Nelson, Petersen, and Tenner. For the classical symmetric group, several properties of these sets have been studied [4,5,8,9,15,17,18]. More recently, the authors of this article characterized and enumerated pinnacle sets for signed permutations [11].…”

Section: Introductionmentioning

confidence: 99%