Bell numbers, their relatives, and algebraic differential equations
Bell numbers, their relatives, and algebraic differential equations
复制标题
DOI：
10.1016/s0097-3165(03)00014-1
复制
发表时间：
2003-04
期刊：
影响因子：
--
通讯作者：
Martin Klazar
中科院分区：
文献类型：
--
作者：
Martin Klazar
我们证明了Bell数的普通母函数不满足C(X)上(实际上，在更大的域上)上的代数微分方程。我们研究了各种集合划分(Uppuluri-Carpenter数、具有j mod I块的划分数、Bessel数、连通划分数和交叉划分数)的相关数，并证明了它们的类似结果。推导了递推、函数方程和连分式展开式。
We prove that the ordinary generating function of Bell numbers satisfies no algebraic differential equation over C (x) (in fact, over a larger field). We investigate related numbers counting various set partitions (the Uppuluri–Carpenter numbers, the numbers of partitions with j mod i blocks, the Bessel numbers, the numbers of connected partitions, and the numbers of crossing partitions) and prove for their ogf's analogous results. Recurrences, functional equations, and continued fraction expansions are derived.