Classification of Connected Shelves
Geometric Topology
2023-07-24 v4 Group Theory
Rings and Algebras
Abstract
We investigate finite right-distributive binary algebraic structures called shelves. We first use symbolic computations with Python to classify (up to isomorphism) all connected shelves with order less than six. We explore the group structure generated by the rows of \textit{latin} shelves. We also define two-variable shelf polynomial by analogy with the quandle polynomial and then state a conjecture about connected idempotent shelves.
Cite
@article{arxiv.2301.12286,
title = {Classification of Connected Shelves},
author = {Mohamed Elhamdadi and Neranga Fernando and Mathew Goonewardena},
journal= {arXiv preprint arXiv:2301.12286},
year = {2023}
}
Comments
18 pages, To appear in New Zealand Journal of Mathematics