Classification of Connected Shelves

Mohamed Elhamdadi; Neranga Fernando; Mathew Goonewardena

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arXiv · 2301.12286

Classification of Connected Shelves

Mohamed Elhamdadi·Neranga Fernando·Mathew Goonewardena

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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.

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Mohamed Elhamdadi, Neranga Fernando, Mathew Goonewardena. 2023-01-28. Classification of Connected Shelves. https://arxiv.org/abs/2301.12286

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