Enumeration of set-theoretic solutions to the Yang-Baxter equation
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.
Citation
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
Publication
Mathematics of Computation
Status
Peer reviewed
ISSN
0025-5718Type
Journal article
Rights
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.
Description
Funding: 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.Collections
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