4-tangrams are 4-avoidable
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908450260254720 |
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| author | Ochem, Pascal Pierron, Théo |
| author_facet | Ochem, Pascal Pierron, Théo |
| contents | A tangram is a word in which every letter occurs an even number of times. Thus it can be cut into parts that can be arranged into two identical words. The \emph{cut number} of a tangram is the minimum number of required cuts in this process. Tangrams with cut number one corresponds to squares. For $k\ge1$, let $t(k)$ denote the minimum size of an alphabet over which an infinite word avoids tangrams with cut number at most~$k$. The existence of infinite ternary square-free words shows that $t(1)=t(2)=3$. We show that $t(3)=t(4)=4$, answering a question from Dębski, Grytczuk, Pawlik, Przybyło, and Śleszyńska-Nowak. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 4-tangrams are 4-avoidable Ochem, Pascal Pierron, Théo Combinatorics Discrete Mathematics A tangram is a word in which every letter occurs an even number of times. Thus it can be cut into parts that can be arranged into two identical words. The \emph{cut number} of a tangram is the minimum number of required cuts in this process. Tangrams with cut number one corresponds to squares. For $k\ge1$, let $t(k)$ denote the minimum size of an alphabet over which an infinite word avoids tangrams with cut number at most~$k$. The existence of infinite ternary square-free words shows that $t(1)=t(2)=3$. We show that $t(3)=t(4)=4$, answering a question from Dębski, Grytczuk, Pawlik, Przybyło, and Śleszyńska-Nowak. |
| title | 4-tangrams are 4-avoidable |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2502.20774 |