On the number of squares in a finite word
Combinatorics
2022-04-27 v2
Abstract
A {\em square} is a word of the form . In this paper we prove that for a given finite word , the number of distinct square factors of is bounded by , where denotes the length of and denotes the number of distinct letters in . This result answers a conjecture of Fraenkel and Simpson stated in 1998.
Cite
@article{arxiv.2204.10204,
title = {On the number of squares in a finite word},
author = {Srečko Brlek and Shuo Li},
journal= {arXiv preprint arXiv:2204.10204},
year = {2022}
}