Geodesic
Algebraic characterization of dendricity
France Gheeraert1 ; Herman Goulet-Ouellet2 ; Julien Leroy3 ; Pierre Stas3
1Université de Picardie Jules Verne
2Czech Technical University in Prague
3University of Liège
The electronic journal of combinatorics, Tome 32 (2025) no. 1
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Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In this paper, we prove its converse, providing the following natural algebraic perspective on dendricity: A minimal shift space is dendric if and only if every set of return words is a basis of the free group over the alphabet.
DOI : 10.37236/13326
Classification : 37B10, 54F50, 68R15
Mots-clés : alphabet, dendric space, language, minimal shift space, return set, word

France Gheeraert  1   ; Herman Goulet-Ouellet  2   ; Julien Leroy  3   ; Pierre Stas  3

1 Université de Picardie Jules Verne
2 Czech Technical University in Prague
3 University of Liège 
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     title = {Algebraic characterization of dendricity},
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France Gheeraert; Herman Goulet-Ouellet; Julien Leroy; Pierre Stas. Algebraic characterization of dendricity. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/13326

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