与Lah-Bell数和多项式相关的完全和不完全Bell多项式
Complete and incomplete Bell polynomials associated with Lah-Bell numbers and polynomials
摘要：
第n个r-扩展的Lah-Bell数被定义为具有$n+r$元素的集合可以被划分成有序块的方式的数量，使得r个区分的元素必须在不同的有序块中。本文的目的是引入不完全r-扩展Lah-Bell多项式和完全$r$ -扩展Lah-Bell多项式分别作为$r$ -Lah数和r-扩展Lah-Bell数的多元形式，并研究这些多项式的一些性质和恒等式.通过这些研究，我们得到了r-Lah数和r-推广的Lah-Bell数作为有限和的一些表达式。
英文摘要：
The nth r-extended Lah-Bell number is defined as the number of ways a set with $n+r$ elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah-Bell polynomials and complete $r$-extended Lah-Bell polynomials respectively as multivariate versions of $r$-Lah numbers and the r-extended Lah-Bell numbers and to investigate some properties and identities for these polynomials. From these investigations, we obtain some expressions for the r-Lah numbers and the r-extended Lah-Bell numbers as finite sums.
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