Pattern occurrences in k-ary words revisited: A few new and old observations

Toufik Mansour; Reza Rastegar

doi:10.1016/j.jcta.2022.105596

Pattern occurrences in k-ary words revisited: A few new and old observations

Toufik Mansour, Reza Rastegar

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the pattern occurrence in k-ary words. We prove an explicit upper bound on the number of k-ary words avoiding any given pattern using a random walk argument. Additionally, we reproduce one already known result on the exponential rate of growth of pattern occurrence in words and establish a simple connection among pattern occurrences in permutations and k-ary words. A simple yet interesting consequence of this connection is that the Wilf-equivalence of two patterns in words implies their Wilf-equivalence in permutations.

Original language	English
Article number	105596
Journal	Journal of Combinatorial Theory. Series A
Volume	188
DOIs	https://doi.org/10.1016/j.jcta.2022.105596
State	Published - May 2022

Bibliographical note

Funding Information:
R.R. would like to thank Alex Roitershtein for many fruitful conversations on the pattern avoidance and occurrence. We also would like to thank Zachary Hunter for pointing out a gap in the proof of Theorem 1.1 in an earlier draft of this paper.

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Pattern avoidance and occurrence
Permutations
Random walk
k-ary words

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2022.105596

Cite this

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abstract = "In this paper, we study the pattern occurrence in k-ary words. We prove an explicit upper bound on the number of k-ary words avoiding any given pattern using a random walk argument. Additionally, we reproduce one already known result on the exponential rate of growth of pattern occurrence in words and establish a simple connection among pattern occurrences in permutations and k-ary words. A simple yet interesting consequence of this connection is that the Wilf-equivalence of two patterns in words implies their Wilf-equivalence in permutations.",

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Pattern occurrences in k-ary words revisited: A few new and old observations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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