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arXiv 2008.044832020-08math.GRmath.QA

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

Ö. Akgün, M. Mereb, L. Vendramin

备注：: 13 pages, 8 tables. Accepted for publication in Mathematics of Computation
发表信息：: Math. Comp. 91 (2022), no. 335, 1469-1481
DOI：: 10.1090/mcom/3696

英文摘要：

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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