Balanced rectangles over Sturmian words and minimal discrepancy intervals
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915941514739712 |
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| author | Vukusic, Ingrid |
| author_facet | Vukusic, Ingrid |
| contents | We consider $m\times n$ rectangular matrices formed from Sturmian words with slope $α$, and we fully characterise their balance properties in terms of the Ostrowski representations of $m$ and $n$ with respect to $α$. This generalises recent results by Anselmo et al., as well as those by Shallit and the author, where only quadratic irrational slopes were considered. In contrast to the two mentioned papers, the approach in this paper is based on the distribution of $nα\bmod 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12801 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Balanced rectangles over Sturmian words and minimal discrepancy intervals Vukusic, Ingrid Number Theory Combinatorics 11J71, 68R15, 11J70 We consider $m\times n$ rectangular matrices formed from Sturmian words with slope $α$, and we fully characterise their balance properties in terms of the Ostrowski representations of $m$ and $n$ with respect to $α$. This generalises recent results by Anselmo et al., as well as those by Shallit and the author, where only quadratic irrational slopes were considered. In contrast to the two mentioned papers, the approach in this paper is based on the distribution of $nα\bmod 1$. |
| title | Balanced rectangles over Sturmian words and minimal discrepancy intervals |
| topic | Number Theory Combinatorics 11J71, 68R15, 11J70 |
| url | https://arxiv.org/abs/2602.12801 |