Year: 2026
Type: preprint
Abstract: A square is a word $xx$, where $x$ is nonempty. We show that a circular word of length $n$ contains at most $\lfloor 3n/2 \rfloor$ distinct squares of length at most $n$. The proof combines known results relating squares to circuits in Rauzy graphs. The coefficient $3/2$ agrees with the known lower bound.
Source: arXiv (Cornell University)
Author: Hamai, Rikuya
Institution: Kyushu University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214758226