Equations and Theories in Plactic Monoids

Turaev, Daniel (2024) Equations and Theories in Plactic Monoids. Masters thesis, University of East Anglia.

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Abstract

In this thesis we explore Diophantine equations and first order sentences of the plactic monoids. We present explicit algebraic criteria for certain small equations to have solutions in the plactic monoids. We also construct an interpretation of a plactic monoid of arbitrary finite rank in Presburger arithmetic, which is known to have decidable first order theory, thereby proving that a plactic monoid of any finite rank will have decidable first order theory. This resolves other open decidability problems about the finite rank plactic monoids, such as the Diophantine problem and identity checking. The algorithm generating the interpretations is uniform, which we use to explore the decidability of the Diophantine problem for the infinite rank plactic monoid. We also prove that the interpretation of the plactic monoids into Presburger Arithmetic is in fact a bi-interpretation, hence any two plactic monoids of finite rank are bi-interpretable with one another.

Item Type:	Thesis (Masters)
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
Depositing User:	Chris White
Date Deposited:	13 Nov 2024 10:32
Last Modified:	13 Nov 2024 10:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/97676
DOI:

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