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

Ö. Akgün; M. Mereb; L. Vendramin

doi:10.1090/mcom/3696

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

Ö. Akgün, M. Mereb, 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 321931 involutive solutions of size nine, 4895272 involutive solutions of size ten and 422449480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.

Original language	English
Journal	Mathematics of Computation
Volume	Early View
DOIs	https://doi.org/10.1090/mcom/3696
Publication status	Published - 14 Jan 2022

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Copyright © 2022 American Mathematical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1090/mcom/3696.
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https://arxiv.org/abs/2008.04483

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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 321931 involutive solutions of size nine, 4895272 involutive solutions of size ten and 422449480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles. ",

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AU - Vendramin, L.

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N2 - 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 321931 involutive solutions of size nine, 4895272 involutive solutions of size ten and 422449480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.

AB - 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 321931 involutive solutions of size nine, 4895272 involutive solutions of size ten and 422449480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.

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VL - Early View

JO - Mathematics of Computation

JF - Mathematics of Computation

ER -

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

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