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Main Authors: Faroß, Nicolas, Volz, Sebastian
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2502.05373
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author Faroß, Nicolas
Volz, Sebastian
author_facet Faroß, Nicolas
Volz, Sebastian
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_05373
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Algorithmic Problems in Categories of Partitions
Faroß, Nicolas
Volz, Sebastian
Data Structures and Algorithms
Quantum Algebra
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.
title Algorithmic Problems in Categories of Partitions
topic Data Structures and Algorithms
Quantum Algebra
url https://arxiv.org/abs/2502.05373