Pinnacle set properties

Domagalski, Rachel; Liang, Jinting; Minnich, Quinn; Sagan, Bruce E.; Schmidt, Jamie; Sietsema, Alexander

doi:10.1016/j.disc.2022.112882

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Lemma 22 a Stirling Permutation Of Order N Can Have At Most1

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2023

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Cited by 3 publications

(2 citation statements)

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“…While there can be multiple witness Stirling permutations for a given admissible mesa set, we often refer to a particular witness Stirling permutation that we call "canonical." This will mimic the terminology used in [3,5,11].…”

Section: Lemma 22 a Stirling Permutation Of Order N Can Have At Mostmentioning

confidence: 99%

“…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%

See 1 more Smart Citation

Pinnacle sets of signed permutations

González

Harris

Kirby

et al. 2023

Discrete Mathematics

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Section: Lemma 22 a Stirling Permutation Of Order N Can Have At Mostmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pinnacle sets of signed permutations

González

Harris

Kirby

et al. 2023

Discrete Mathematics

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Further results on pinnacle sets

Minnich

2023

Discrete Mathematics

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Efficient recurrence for the enumeration of permutations with fixed pinnacle set

Fang¹

2022

Discrete Mathematics &Amp; Theoretical Computer Science

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Initiated by Davis, Nelson, Petersen and Tenner (2018), the enumerative study of pinnacle sets of permutations has attracted a fair amount of attention recently. In this article, we provide a recurrence that can be used to compute efficiently the number $|\mathfrak{S}_n(P)|$ of permutations of size $n$ with a given pinnacle set $P$, with arithmetic complexity $O(k^4 + k\log n)$ for $P$ of size $k$. A symbolic expression can also be computed in this way for pinnacle sets of fixed size. A weighted sum $q_n(P)$ of $|\mathfrak{S}_n(P)|$ proposed in Davis, Nelson, Petersen and Tenner (2018) seems to have a simple form, and a conjectural form is given recently by Flaque, Novelli and Thibon (2021+). We settle the problem by providing and proving an alternative form of $q_n(P)$, which has a strong combinatorial flavor. We also study admissible orderings of a given pinnacle set, first considered by Rusu (2020) and characterized by Rusu and Tenner (2021), and we give an efficient algorithm for their counting.

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Pinnacle set properties

Cited by 3 publications

References 7 publications

Pinnacle sets of signed permutations

Pinnacle sets of signed permutations

Further results on pinnacle sets

Efficient recurrence for the enumeration of permutations with fixed pinnacle set

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