Finite Diagram Semigroups: Extending the Computational Horizon

TL;DR

This paper broadens the understanding of diagram semigroups by establishing a general framework and expanding computational data, revealing surprising patterns and raising new theoretical questions.

Contribution

It introduces a unified framework for diagram semigroups and significantly extends computational analysis, uncovering novel observations and open research questions.

Findings

Rich computational data set with surprising patterns

Identification of open questions for future research

Extension of the computational horizon for diagram semigroups

Abstract

Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our computational knowledge of them. The generated data set is replete with surprising observations raising many open questions for further theoretical research.