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arXiv · 2502.05373

Algorithmic Problems in Categories of Partitions

Nicolas Faroß·Sebastian Volz
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Abstract

Categories of partitions are combinatorial structures arising from the representation theory of certain compact quantum groups and are linked to classical diagram algebras such as the Temperley-Lieb algebra. In this paper, we present efficient algorithms and data-structures for partitions of sets and their corresponding category operations, including a concrete implementation in the computer algebra system OSCAR. Moreover, we show that there exists a category of partitions for which the natural computational problems of deciding membership of a given partition as well as counting partitions of a given size are algorithmically undecidable.

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Nicolas Faroß, Sebastian Volz. 2025-02-07. Algorithmic Problems in Categories of Partitions. https://arxiv.org/abs/2502.05373

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