Circularly squarefree words and unbordered conjugates: a new approach
Formal Languages and Automata Theory
2019-04-18 v1 Discrete Mathematics
Combinatorics
Abstract
Using a new approach based on automatic sequences, logic, and a decision procedure, we reprove some old theorems about circularly squarefree words and unbordered conjugates in a new and simpler way. Furthermore, we prove three new results about unbordered conjugates: we complete the classification, due to Harju and Nowotka, of binary words with the maximum number of unbordered conjugates; we prove that for every possible number, up to the maximum, there exists a word having that number of unbordered conjugates, and finally, we determine the expected number of unbordered conjugates in a random word.
Keywords
Cite
@article{arxiv.1904.08187,
title = {Circularly squarefree words and unbordered conjugates: a new approach},
author = {Trevor Clokie and Daniel Gabric and Jeffrey Shallit},
journal= {arXiv preprint arXiv:1904.08187},
year = {2019}
}