标题： 算法问题在分划范畴中 显示英文标题

标题： Algorithmic Problems in Categories of Partitions

摘要： 划分的类别是来自某些紧致量子群表示理论的组合结构，并与经典的图示代数如Temperley-Lieb代数相关联。 在本文中，我们提出了用于集合划分及其相应范畴运算的高效算法和数据结构，包括在计算机代数系统OSCAR中的具体实现。 此外，我们表明存在一个划分的范畴，其中判断给定划分是否属于该范畴以及计算给定大小的划分数量的自然计算问题在算法上是不可判定的。 显示英文摘要

摘要： 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.