A natural bijection for contiguous pattern avoidance in words
Combinatorics
2023-12-04 v2 Discrete Mathematics
Formal Languages and Automata Theory
Abstract
Two words and are avoided by the same number of length- words, for all , precisely when and have the same set of border lengths. Previous proofs of this theorem use generating functions but do not provide an explicit bijection. We give a bijective proof for all pairs that have the same set of proper borders, establishing a natural bijection from the set of words avoiding to the set of words avoiding .
Cite
@article{arxiv.2212.08959,
title = {A natural bijection for contiguous pattern avoidance in words},
author = {Julia Carrigan and Isaiah Hollars and Eric Rowland},
journal= {arXiv preprint arXiv:2212.08959},
year = {2023}
}
Comments
This version is our accepted manuscript. The most important changes from the previous version are as follows. The proof of the main theorem is streamlined, the introduction is updated, and section 4 is omitted. (12 pages, 8 figures)