论文标题
$ q的分析方面，r $ $ - 两种元素数字的动态
Analytic aspects of $q,r$-analogue of poly-Stirling numbers of both kinds
论文作者
论文摘要
第二种计数签名的设置分区的$ b $的Stirling数字。在本文中，我们提供了有关这些数字的新组合和分析身份，以及Broder对这些数字的$ r $转换。在这些身份中，可以找到递归，基于包含 - 排斥原理的明确公式，以及指数产生的函数。 这些斯特林数字可以被视为使用Comtet和Lancaster的结果来表征的更广泛的三角形家族的成员。 我们将这些定理概括为，这些定理呈现出等效的条件，将数字的三角形作为一般性的Stirling数字的三角形，以$ q，r $ $ $ $ - poly-poly stirl数字，这些数字是$ q $ q $ - 由broder定义的受限制的stirl数字的$ q $ - 分析，并在其定义的恢复中出现了多功能值。有两种方法可以做到这一点，这些方式通过一个很好的身份相关。
The Stirling numbers of type $B$ of the second kind count signed set partitions. In this paper we provide new combinatorial and analytical identities regarding these numbers as well as Broder's $r$-version of these numbers. Among these identities one can find recursions, explicit formulas based on the inclusion-exclusion principle, and also exponential generating functions. These Stirling numbers can be considered as members of a wider family of triangles of numbers that are characterized using results of Comtet and Lancaster. We generalize these theorems, which present equivalent conditions for a triangle of numbers to be a triangle of generalized Stirling numbers, to the case of the $q,r$-poly Stirling numbers, which are $q$-analogues of the restricted Stirling numbers defined by Broder and having a polynomial value appearing in their defining recursion. There are two ways to do this and these ways are related by a nice identity.
