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arXiv · 2001.07325

A formula for enumerating permutations with a fixed pinnacle set

Alexander Diaz-Lopez·Pamela E. Harris·Isabella Huang·Erik Insko·Lars Nilsen
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Abstract

In 2017 Davis, Nelson, Petersen, and Tenner pioneered the study of pinnacle sets of permutations and asked whether there exists a class of operations, which applied to a permutation in $\mathfrak{S}_n$, can produce any other permutation with the same pinnacle set and no others. In this paper, we adapt a group action defined by Foata and Strehl to provide a way to generate all permutations with a given pinnacle set. From this we give a closed non-recursive formula enumerating permutations with a given pinnacle set. Thus answering a question posed by Davis, Nelson, Petersen, and Tenner.

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Alexander Diaz-Lopez, Pamela E. Harris, Isabella Huang, Erik Insko, Lars Nilsen. 2020-01-21. A formula for enumerating permutations with a fixed pinnacle set. https://arxiv.org/abs/2001.07325

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