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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.17987 |
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Table of Contents:
- Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct definition of multipermutation solutions has not been established so far. We fill here this gap providing a definition of multipermutation solutions that generalizes the one for non-degenerate solutions and we find an axiomatic description of this class by a set of equations that generalizes the equations describing non-degenerate multipermutation solutions. It turned out that the results do not need all the properties of solutions of the Yang-Baxter equation and therefore we prove them in a general universal-algebraic setting.