A Lebesgue variant of the additive square problem
Combinatorics
2025-06-27 v1
Abstract
The additive square problem is a relatively famous open problem in the area of combinatorics on words: Does there exist an infinite word over a finite alphabet, such that no two consecutive blocks of the same length have the same sum? In this note we solve a Lebesgue integral variant of the problem. The proof is based on Lebesgue's density theorem.
Cite
@article{arxiv.2506.21200,
title = {A Lebesgue variant of the additive square problem},
author = {Ingrid Vukusic},
journal= {arXiv preprint arXiv:2506.21200},
year = {2025}
}
Comments
5 pages