Binary Words Containing Few Abelian Squares
Combinatorics
2026-04-28 v1 Discrete Mathematics
Abstract
Fici and Saarela ([2]) conjectured that a binary word of length n contains at least abelian squares. We slightly extend this conjecture and show that it holds in some special cases. In all other cases we have the following: given a Parikh vector over a two letter alphabet we produce a word with that Parikh vector which we conjecture contains the least possible number of abelian squares.
Cite
@article{arxiv.2604.23188,
title = {Binary Words Containing Few Abelian Squares},
author = {Szilard Zsolt Fazekas and Adam Mammoliti and Robert Mercas and Jamie Simpson},
journal= {arXiv preprint arXiv:2604.23188},
year = {2026}
}