Hsu-Riordan 阵/partial monoid(英文)

Hsu-Riordan Array/Partial Monoid

中文关键词:  Riordan阵/徐-Riordan阵  偏monoid  发生函数  stirling数  转换公式  恒等式

英文关键词:Riordan array/Hsu-Riordan array  partial monoid  generating functon  Stirling numbers  transfer formula  identity

中文摘要:

      本文首先对Shapiro的Riordan群进行了推广,给出了Hsu-Riordan partialmonoid的概念,然后在此框架内,对徐利治先生的两类扩展型广义Stirling数偶进行了统一处理;建立了Hsu-Wang转换定理,Brown-Sprugnoli转换公式,以及广义Brown转换引理-它揭示了一些不同类型的Hsu-Riordan阵之间转换的方法,由此可产生大量的恒等式.

英文摘要:

      This paper gives a unified approach to Hsu's two classes of extended GSN pairs in the setting of Hsu-Riordan partial monoid which is a generalization of Shapiro's Riordan group, and moreover Hsu-Wang transfer theorem, Drown-Sprugnoli transfer formula and generalized Brown transfer lemma which display some transfer methods of different kinds of Hsu-Riordau arrays and identities respectively.