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arXiv · 2506.21200

A Lebesgue variant of the additive square problem

Ingrid Vukusic
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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.

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Ingrid Vukusic. 2025-06-26. A Lebesgue variant of the additive square problem. https://arxiv.org/abs/2506.21200

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