Algebraic Characterization of Dendricity
Authors
Gheeraert, F.; Goulet-Ouellet, H.; Leroy, J.; Stas, P.
Year
2025
Published
The Electronic Journal of Combinatorics. 2025, 32(1), 1-8. ISSN 1077-8926.
Type
Article
DOI
Departments
Annotation
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
Authors
Berthé, V.; Goulet-Ouellet, H.
Year
2024
Published
Theory of Computing Systems. 2024, 68(6), 1512-1536. ISSN 1432-4350.
Type
Article
Departments
Annotation
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.