论文标题
通过玻色子操作员，堕落的R-striring数字上的某些身份
Some identities on degenerate r-stirling numbers via boson operators
论文作者
论文摘要
布罗德（Broder）介绍了第一种和第二种的R-striring数字，这些数字列举了限制的排列和限制分区，其限制是第一个R元素必须分别以不同的周期为单位，并且在不同的子集中分别为不同的周期。 Kim-kim-lee-park构建了两种堕落的R-stirling数字，作为它们的退化版本。本文的目的是通过Boson Operators来得出第一类和第二类的R-STIRL数字的某些身份和复发关系。特别是，我们获得了数量运算符的退化积分功率的正常排序，乘以创建玻色子算子的积分功率，而玻色子算子的玻色子算子的含量为boson operators，其中第二种退化的R-striring数字显示为系数。
Broder introduced the r-Stirling numbers of the first kind and of the second kind which enumerate restricted permutations and respectively restricted partitions, the restriction being that the first r elements must be in distinct cycles and respectively in distinct subsets. Kim-Kim-Lee-Park constructed the degenerate r-Stirling numbers of both kinds as degenerate versions of them. The aim of this paper is to derive some identities and recurrence relations for the degenerate r-Stirling numbers of the first kind and of the second kind via boson operators. In particular, we obtain the normal ordering of a degenerate integral power of the number operator multiplied by an integral power of the creation boson operator in terms of boson operators where the degenerate r-Stirling numbers of the second kind appear as the coefficients.
