## Enumeration of set-theoretic solutions to the Yang–Baxter equation

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Ö. Akgün, M. Mereb and L. Vendramin
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## Abstract:

We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions to the Yang–Baxter equation of small size. We show that there are 321,931 involutive solutions of size nine, 4,895,272 involutive solutions of size ten and 422,449,480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.## References

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## Additional Information

**Ö. Akgün**- Affiliation: School of Computer Science, University of St Andrews, St Andrews, Fife KY16 9SX, United Kingdom
- ORCID: 0000-0001-9519-938X
- Email: ozgur.akgun@st-andrews.ac.uk
**M. Mereb**- Affiliation: IMAS–CONICET and Depto. de Matemática, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina
- MR Author ID: 870581
- Email: mmereb@dm.uba.ar
**L. Vendramin**- Affiliation: IMAS–CONICET and Depto. de Matemática, FCEN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina; and Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
- MR Author ID: 829575
- ORCID: 0000-0003-0954-7785
- Email: lvendramin@dm.uba.ar, leandro.vendramin@vub.be
- Received by editor(s): September 14, 2020
- Received by editor(s) in revised form: June 7, 2021, and August 11, 2021
- Published electronically: January 14, 2022
- Additional Notes: The second author was partially supported by PICT 2018-3511 and is also a Junior Associate of the ICTP. The third author was supported by NYU-ECNU Institute of Mathematical Sciences at NYU–Shanghai and was supported in part by PICT 2016-2481 and UBACyT 20020170100256BA
- © Copyright 2022 American Mathematical Society
- Journal: Math. Comp.
**91**(2022), 1469-1481 - MSC (2020): Primary 16T25; Secondary 81R50
- DOI: https://doi.org/10.1090/mcom/3696
- MathSciNet review: 4405502