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The construction of multipermutation solutions of the Yang-Baxter equation of level 2

We study involutive set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2. These solutions happen to fall into two classes -- distributive ones and non-distributive ones. The distributive ones can be effectively constructed using a set of abelian groups and a matrix of constants. Using this construction, we enumerate all distributive involutive solutions up to size 14. The non-distributive solutions can be also easily constructed, using a distributive solution and a permutation.

preprint2019arXivOpen access
Přemysl JedličkaAgata PilitowskaAnna Zamojska-Dzienio
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Open access3 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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Přemysl JedličkaAgata PilitowskaAnna Zamojska-Dzienio

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