A290887 The number of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation of order n up to isomorphism.

1, 2, 5, 23, 88, 595, 3456, 34530, 321931, 4895272

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Özgur Akgun, Martin Mereb, and Leandro Vendramin, Enumeration of set-theoretic solutions to the Yang-Baxter equation, arXiv:2008.04483 [math.GR], 2020.

Özgur Akgun, Mun See Chang, Ian P. Gent, and Christopher Jefferson, Breaking the Symmetries of Indistinguishable Objects, arXiv:2503.17251 [cs.AI], 2025. See pp. 14, 17.

Marco Bonatto, Michael Kinyon, David Stanovský, and Petr Vojtěchovský, Involutive Latin solutions of the Yang-Baxter equation, arXiv:1910.02148 [math.GR], 2019.

Pavel Etingof, Travis Schedler, and Alexandre Soloviev, Set-theoretical solutions to the quantum Yang-Baxter equation, arXiv:math/9801047 [math.QA], 1998; Duke Math. J. 100 (1999), no. 2, 169-209.

Crossrefs

Sequence in context: A106858 A380852 A376156 * A219889 A369834 A100299

Adjacent sequences: A290884 A290885 A290886 * A290888 A290889 A290890

Keyword

nonn,hard,more

Author

David Stanovsky, Aug 13 2017

Extensions

a(8) corrected and a(9)-a(10) added by Leandro Vendramin, Aug 15 2020

Status

approved