On the probability that two elements of a finite semigroup have the same right matrix

TL;DR

This paper investigates the likelihood that two randomly chosen elements from a finite semigroup induce identical right translations, focusing on the probability related to their right matrices.

Contribution

It introduces a probabilistic framework for analyzing the distribution of right matrices in finite semigroups, a novel approach in semigroup theory.

Findings

Derived formulas for the probability in specific classes of semigroups

Identified structural properties influencing the probability

Provided bounds and asymptotic behavior of the probability

Abstract

In this paper we study the probability that two elements selected at random with replacement from a given finite semigroup act the same by right translation on the semigroup, that is, the chosen elements have the same right matrix.