Semigroup identities of supertropical matrices

TL;DR

This paper proves that all supertropical matrices of a given size satisfy nontrivial semigroup identities, linking algebraic properties to graph-theoretic walk structures.

Contribution

It establishes the existence of nontrivial semigroup identities for supertropical matrices of any size, extending tropical matrix theory.

Findings

Supertropical matrices satisfy nontrivial semigroup identities.

Identities are applicable to walks on labeled-weighted digraphs with double arcs.

Results connect algebraic identities with graph walk properties.

Abstract

We prove that, for any $n$, the monoid of all $n \times n$ supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities. These identities are carried over to walks on labeled-weighted digraphs with double arcs.