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arXiv · 2407.00755

Non-involutive solutions of the Yang-Baxter equation of multipermutation level 2

Jan Hora·Premysl Jedlicka·Agata Pilitowska
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Abstract

We study non-degenerate set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2 which are not 2-reductive. We describe an effective way of constructing such solutions using square-free 2-reductive solutions and two bijections. We present an algorithm how to obtain all such finite solutions, up to isomorphism. Using this algorithm, we enumerate all solutions of multipermutation level 2 up to size 6.

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Jan Hora, Premysl Jedlicka, Agata Pilitowska. 2024-06-30. Non-involutive solutions of the Yang-Baxter equation of multipermutation level 2. https://arxiv.org/abs/2407.00755

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