欧拉数、戴煦数与齿排列的关系研究

Research on the Relations Between Euler Numbers, Dai Xu Numbers and Gear Mutation

对欧拉数、戴煦数与齿排列的关系进行研究,揭示了欧拉数与戴煦数都是一对相辅相成、难解难分的函数,比伯努利数与欧拉数的关系更进一步;在齿排列中赋予了戴煦数和欧拉数明确的组合意义,并使两者统一于安德烈数,安德烈数是欧拉数与戴煦数的复合,这一性质简单优美,是伯努利数所不具备的。

This paper reveals that Euler numbers and Dai Xu numbers are more relevant and inseparable function to each other when they are compared with Bernoulli numbers and Euler numbers.In gear permutation,it gives a combination meaning to Euler numbers and Dai Xu numbers.Andre numbers are a compound of Euler numbers and Dai Xu numbers,whose nature is simple and perfect and not possessed by Bernoulli numbers.