Year: 2026
Type: article
Abstract: In this article, we study word equations in free semigroups and the conjecture that the existence of infinitely many solutions entails the existence of solutions with arbitrarily large exponent of periodicity. We examine this question in the broader framework of word equations with regular constraints and establish new positive results: the conjecture holds for all quadratic word equations with constraints in finite semigroups from the variety $$\textbf{DLG}$$ DLG and its dual $$\textbf{DRG}$$ DRG , encompassing all finite groups, commutative semigroups, and $$\mathcal {J}$$ J -trivial semigroups.
Source: Semigroup Forum
Institutions: University of Stuttgart, University of Siegen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4416184885
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