Semigroup Forum· 2026Q2
Quadratic word equations with regular constraints and the exponent of periodicity
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- Q2SCImago
- 2026year
Short summary
The conjecture that infinitely many solutions to word equations imply solutions with arbitrarily large periodicity holds for quadratic word equations with constraints in DLG and DRG finite semigroups.
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Key points
- The conjecture linking infinite solutions to arbitrarily large periodicity is studied for word equations.
- New positive results confirm the conjecture for quadratic word equations with regular constraints.
- The findings apply to finite semigroups in the DLG and DRG varieties.
- This includes structures like finite groups, commutative semigroups, and J-trivial semigroups.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Semigroup Forum, 2026 · DOI ↗
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Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science