带限制的Bell数和阶乘数的组合和算术性质
Combinatorial and Arithmetical Properties of the Restricted and Associated Bell and Factorial Numbers
摘要：
对块和圈的大小有限制的集合划分和置换是重要的组合序列。计数这些对象导致的序列推广的经典斯特林和贝尔号码。本文的重点是分析它们的组合性质和算术性质。结果包括几个组合恒等式和递归式以及它们的$p$ -adic赋值的一些性质。
英文摘要：
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus of the present article is the analysis of combinatorial and arithmetical properties of them. The results include several combinatorial identities and recurrences as well as some properties of their $p$-adic valuations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
