Binary Words Containing Few Abelian Squares
arXiv:2604.2318841.1
AI Analysis
Advances understanding of combinatorial properties of binary words, but results are partial and conjectural.
The authors investigate a conjecture about the minimum number of abelian squares in binary words, proving it for special cases and proposing a construction for the general case.
Fici and Saarela ([2]) conjectured that a binary word of length n contains at least $\lfloor n/4 \rfloor$ 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.