The idempotent generated subsemigroup of the Kauffman monoid

TL;DR

This paper characterizes the idempotent generated subsemigroup of the Kauffman monoid using combinatorial data, and determines the minimal sizes of generating and idempotent generating sets.

Contribution

It provides a combinatorial description of the subsemigroup and computes the minimal generating sets, advancing understanding of the algebraic structure of the Kauffman monoid.

Findings

Characterization of elements via normal forms

Calculation of smallest generating set size

Determination of minimal idempotent generating set size

Abstract

We characterise the elements of the (maximum) idempotent generated subsemigroup of the Kauffman monoid in terms of combinatorial data associated to certain normal forms. We also calculate the smallest size of a generating set and idempotent generating set.