Binary Words Containing Few Abelian Squares
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910165774630912 |
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| author | Fazekas, Szilard Zsolt Mammoliti, Adam Mercas, Robert Simpson, Jamie |
| author_facet | Fazekas, Szilard Zsolt Mammoliti, Adam Mercas, Robert Simpson, Jamie |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Binary Words Containing Few Abelian Squares Fazekas, Szilard Zsolt Mammoliti, Adam Mercas, Robert Simpson, Jamie Combinatorics Discrete Mathematics G.2.1 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. |
| title | Binary Words Containing Few Abelian Squares |
| topic | Combinatorics Discrete Mathematics G.2.1 |
| url | https://arxiv.org/abs/2604.23188 |