Alexander Burstein - Distribution of sets of descent tops and descent bottoms on restricted permutations

dmtcs:12636 - Discrete Mathematics & Theoretical Computer Science, January 14, 2025, vol. 26:1, Permutation Patterns 2023 - https://doi.org/10.46298/dmtcs.12636
Distribution of sets of descent tops and descent bottoms on restricted permutationsArticle

Authors: Alexander Burstein

In this note, we prove some and conjecture other results regarding the distribution of descent top and descent bottom sets on some pattern-avoiding permutations. In particular, for 3-letter patterns, we show bijectively that the set of descent tops and the set of descent bottoms are jointly equidistributed on the avoiders of 231 and 312. We also conjecture similar equidistributions for 4-letter patterns, in particular, that the set of descent tops and the set of descent bottoms are jointly equidistributed on the avoiders of 3142, 3241, 4132. This conjecture and several others made in this paper have now been proved by Zhou, Zang, and Yan (2024).

Comment: 16 pages, 3 figures

https://doi.org/10.46298/dmtcs.12636
Source: arXiv.org:2306.08065
Volume: vol. 26:1, Permutation Patterns 2023
Section: Special issues
Published on: January 14, 2025
Accepted on: January 7, 2025
Submitted on: December 2, 2023
Keywords: Mathematics - Combinatorics, 05A05, 05A15
Licence: arXiv.org - Non-exclusive license to distribute

Classifications

Mathematics Subject Classification 20201
Sources:
  • [1] zbMATH Open.

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