Algebraic Characterization of Dendricity
Autoři
Gheeraert, F.; Goulet-Ouellet, H.; Leroy, J.; Stas, P.
Rok
2025
Publikováno
The Electronic Journal of Combinatorics. 2025, 32(1), 1-8. ISSN 1077-8926.
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Článek
DOI
Pracoviště
Anotace
Dendric shift spaces simultaneously generalize co dings 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.
Obstructions to Return Preservation for Episturmian Morphisms
Autoři
Berthé, V.; Goulet-Ouellet, H.
Rok
2024
Publikováno
Theory of Computing Systems. 2024, 68(6), 1512-1536. ISSN 1432-4350.
Typ
Článek
Pracoviště
Anotace
This paper studies obstructions to preservation of return sets by episturmian morphisms. We show, by way of an explicit construction, that infinitely many obstructions exist. This generalizes and improves an earlier result about Sturmian morphisms.