ON THE ENUMERATION OF FINITE L-ALGEBRAS

C. Dietzel; P. Menchón; L. Vendramin

doi:10.1090/MCOM/3814

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 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. © 2023 American Mathematical Society

Original language	English
Pages (from-to)	1363 - 1381
Number of pages	19
Journal	Mathematics of Computation
Volume	92
Issue number	341
DOIs	https://doi.org/10.1090/MCOM/3814
Publication status	Published - 2023

Bibliographical note

Funding Information:
Received by the editor June 15, 2022, and, in revised form, October 21, 2022, and November 14, 2022. 2020 Mathematics Subject Classification. Primary 03G25; Secondary 06D20. 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.

Publisher Copyright:
© 2023 American Mathematical Society

Copyright:
Copyright 2023 Elsevier B.V., All rights reserved.

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10.1090/MCOM/3814

96040919Accepted author manuscript, 420 KBLicence: CC BY

Cite this

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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. {\textcopyright} 2023 American Mathematical Society",

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note = "Funding Information: Received by the editor June 15, 2022, and, in revised form, October 21, 2022, and November 14, 2022. 2020 Mathematics Subject Classification. Primary 03G25; Secondary 06D20. 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. Publisher Copyright: {\textcopyright} 2023 American Mathematical Society Copyright: Copyright 2023 Elsevier B.V., All rights reserved.",

year = "2023",

doi = "10.1090/MCOM/3814",

language = "English",

volume = "92",

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journal = "Mathematics of Computation",

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AU - Vendramin, L.

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N2 - 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. © 2023 American Mathematical Society

AB - 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. © 2023 American Mathematical Society

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SN - 0025-5718

IS - 341

ER -

ON THE ENUMERATION OF FINITE L-ALGEBRAS

Abstract

Bibliographical note

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A database of L-algebras

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ON THE ENUMERATION OF FINITE L-ALGEBRAS

Abstract

Bibliographical note

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A database of L-algebras

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