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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Jan Hora,
  • Přemysl Jedlička,
  • Agata Pilitowska

摘要

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.