On the enumeration of finite $L$-algebras
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- by C. Dietzel, P. Menchón and L. Vendramin;
- Math. Comp. 92 (2023), 1363-1381
- DOI: https://doi.org/10.1090/mcom/3814
- Published electronically: January 23, 2023
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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 377,322,225 isomorphism classes of $L$-algebras of size eight. The database constructed suggests the existence of bijections between certain classes of $L$-algebras and well-known combinatorial objects. We prove that Bell numbers enumerate isomorphism classes of finite linear $L$-algebras. We also prove that finite regular $L$-algebras are in bijective correspondence with infinite-dimensional Young diagrams.References
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Bibliographic Information
- C. Dietzel
- Affiliation: Department of Mathematics and Data Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
- MR Author ID: 1305522
- Email: carstendietzel@gmx.de
- P. Menchón
- Affiliation: Department of Logic, Nicolaus Copernicus University in Toruń, Fosa Staromiejska 1a, 87-100 Toruń, Poland
- ORCID: 0000-0002-9395-107X
- Email: paula.menchon@v.umk.pl
- L. Vendramin
- Affiliation: Department of Mathematics and Data Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
- MR Author ID: 829575
- ORCID: 0000-0003-0954-7785
- Email: Leandro.Vendramin@vub.be
- Received by editor(s): June 15, 2022
- Received by editor(s) in revised form: October 21, 2022, and November 14, 2022
- Published electronically: January 23, 2023
- Additional Notes: This research was supported through the program “Oberwolfach Research Fellows” by the Mathematisches Forschungsinstitut Oberwolfach in 2022. The second author was partially supported by the National Science Center (Poland), grant number 2020/39/B/HS1/00216. The third author was supported in part by OZR3762 of Vrije Universiteit Brussel.
- © Copyright 2023 American Mathematical Society
- Journal: Math. Comp. 92 (2023), 1363-1381
- MSC (2020): Primary 03G25; Secondary 06D20
- DOI: https://doi.org/10.1090/mcom/3814
- MathSciNet review: 4550330