Tropical one-relation monoids
Carl-Fredrik Nyberg-Brodda

TL;DR
This paper classifies all one-relation monoids that can be represented as semigroups of tropical matrices, extending previous results on the bicyclic monoid to a broader class.
Contribution
It provides a complete classification of one-relation monoids admitting tropical matrix representations, with only two exceptions.
Findings
Most one-relation monoids admit tropical matrix representations.
The classification includes all but two specific monoids.
Extends the known representation of the bicyclic monoid to a wider class.
Abstract
In 2010, Izhakian & Margolis proved that the bicyclic monoid admits a representation as a semigroup of upper triangular tropical matrices. We extend this result by classifying all one-relation monoids which admit such representations. We also classify, with two exceptions, all one-relation monoids which admit representations as semigroups of tropical matrices.
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Taxonomy
Topicssemigroups and automata theory
