摘要
互反级数关系是组合数学领域非常重要的计算工具.本文作者之一曾详细研究了单变量互反函数与互反级数变换之间的关系,并讨论了对于组合序列与多项式序列的应用.这里我们将在§1中简单概述互反函数与互反级数关系的基本结果及其变形,并且计算广义Humbert多项式的相伴多项式.作为理论的自然扩充,§2中研究互反矢量函数及相关联的多元互反关系.作为文中主要定理的应用,§3中讨论某些具体的多元互反级数关系及Carlitz和Mohanty卷积恒等式的证明.
A brief survey is given for the relation between reciprocal functions and series inversions. The reciprocal vectorial functions are investigated which yield a kind of multifold inverse series relations. Some concrete examples and the convolution-type identities due to Carlitz and Mohanty are presented as appli-cations.
