Enumeration of set-theoretic solutions to the Yang-Baxter equation
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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.
Akgün , Ö , Mereb , M & Vendramin , L 2022 , ' Enumeration of set-theoretic solutions to the Yang-Baxter equation ' , Mathematics of Computation , vol. Early View . https://doi.org/10.1090/mcom/3696
Mathematics of Computation
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DescriptionFunding: The second author is partially supported by PICT 2018-3511 and is also a Junior Associate of the ICTP. The third author acknowledges support of NYU-ECNU Institute of Mathematical Sciences at NYU–Shanghai and he is supported in part by PICT 2016-2481 and UBACyT 20020170100256BA.
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