Several variants of the Dumont differential system and permutation statistics

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（10）
• 页码范围: 2033-2052
• 页数: 20页
• 语种: 英文

摘要

The Dumont differential system on the Jacobi elliptic functions was introduced by Dumont (1979)and was extensively studied by Dumont,Viennot,Flajolet and so on.In this paper,we first present a labeling scheme for the cycle structure of permutations.We then introduce two types of Jacobi pairs of differential equations.We present a general method to derive the solutions of these differential equations.As applications,we present some characterizations for several permutation statistics.