Critical exponents of infinite balanced words
Combinatorics
2018-01-17 v1 Formal Languages and Automata Theory
Abstract
Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2+sqrt(2)/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5+sqrt(5))/4. Over larger alphabets, we give some candidates for balanced words (found computationally) having small critical exponents. We also explore a method for proving these results using the automated theorem prover Walnut.
Cite
@article{arxiv.1801.05334,
title = {Critical exponents of infinite balanced words},
author = {Narad Rampersad and Jeffrey Shallit and Élise Vandomme},
journal= {arXiv preprint arXiv:1801.05334},
year = {2018}
}
Comments
14 pages