On the enumeration of finite $L$-algebras

C. Dietzel; P. Menchón; L. Vendramin

doi:10.1090/mcom/3814

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arXiv · 2206.04955

On the enumeration of finite $L$-algebras

C. Dietzel·P. Menchón·L. Vendramin

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Abstract

We use Constraint Satisfaction Methods to construct and enumerate finite $L$-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial Yang-Baxter equation. There are 377322225 isomorphism classes of $L$-algebras of size eight. The database constructed suggest the existence of bijections between certain classes of $L$-algebras and well-known combinatorial objects. On the one hand, we prove that Bell numbers enumerate isomorphism classes of finite linear $L$-algebras. On the other hand, we also prove that finite regular $L$-algebras are in bijective correspondence with infinite-dimensional Young diagrams.

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BibTeX RIS

C. Dietzel, P. Menchón, L. Vendramin. 2022-06-10. On the enumeration of finite $L$-algebras. https://doi.org/10.1090/mcom%2F3814

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