English

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.

Keywords

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

R2 v1 2026-07-01T03:34:24.248Z