Semigroup identities in the monoid of triangular tropical matrices

TL;DR

This paper demonstrates that the monoid of triangular tropical matrices satisfies nontrivial semigroup identities and introduces a generic construction for such identities, providing bounds based on Fibonacci numbers.

Contribution

It presents the first known semigroup identities for triangular tropical matrix monoids and offers a method to construct and bound these identities.

Findings

Triangular tropical matrix monoids satisfy nontrivial semigroup identities.

A generic construction method for such identities is provided.

Fibonacci numbers are used to bound the length of identities.

Abstract

We show that the submonoid of all nxn triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities.