4-tangrams are 4-avoidable

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 $...

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Published inDiscrete Mathematics and Theoretical Computer Science Vol. 27:3; no. Combinatorics; pp. 1 - 6
Main Authors Ochem, Pascal, Pierron, Théo
Format Journal Article
LanguageEnglish
Published Nancy DMTCS 01.10.2025
Discrete Mathematics & Theoretical Computer Science
Subjects
combinatorics
Computer Science
discrete mathematics
Mathematical research
Variables
France
Combinatorics on words
Online AccessGet full text
ISSN1365-8050
1462-7264
1365-8050
DOI10.46298/dmtcs.15310

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Summary: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.
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ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.15310