Pattern occurrences in $k$-ary words revisited: a few new and old observations
Combinatorics
2022-12-22 v5
Abstract
In this paper, we study the pattern occurrence in -ary words. We prove an explicit upper bound on the number of -ary words avoiding any given pattern using a random walk argument. Additionally, we reproduce several already known results and establish a simple connection among pattern occurrences in permutations and -ary words. A simple consequence of this connection is that Wilf-equivalence of two patterns in words implies their Wilf-equivalence in permutations.
Cite
@article{arxiv.2102.00443,
title = {Pattern occurrences in $k$-ary words revisited: a few new and old observations},
author = {Toufik Mansour and Reza Rastegar},
journal= {arXiv preprint arXiv:2102.00443},
year = {2022}
}
Comments
Lemma 2.2 is added to close an existing gap in the proof of Theorem 1.1 in an earlier version of the paper