This survey is intended to provide an overview of one of the oldest and most celebrated
open problems in combinatorial algebra: the word problem for one-relation monoids. We …

In this paper, we begin the systematic study of group equations with abelian predicates in
the main classes of groups where solving equations is possible. We extend the line of work …

In this paper we study the satisfiability and solutions of group equations when combinatorial,
algebraic and language-theoretic constraints are imposed on the solutions. We show that …

We study the Diophantine problem, ie the decision problem of solving systems of equations,
for some families of one-relator groups, and provide some background for why this problem …

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The Diophantine problem for a monoid M is the decision problem to decide whether any
given system of equations has a solution in M. In this short note, we give a simple example …

This article studies the properties of word-hyperbolic semigroups and monoids, that is, those
having context-free multiplication tables with respect to a regular combing, as defined by …

We prove that a plactic monoid of any finite rank has decidable first order theory. This
resolves other open decidability problems about the finite rank plactic monoids, such as the …

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 …