Several variants of the Dumont differential system and permutation statistics

Shi Mei Ma; Toufik Mansour; David G.L. Wang; Yeong Nan Yeh

doi:10.1007/s11425-016-9240-5

Several variants of the Dumont differential system and permutation statistics

Shi Mei Ma, Toufik Mansour, David G.L. Wang, Yeong Nan Yeh^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2033-2052
Number of pages	20
Journal	Science China Mathematics
Volume	62
Issue number	10
DOIs	https://doi.org/10.1007/s11425-016-9240-5
Publication status	Published - 1 Oct 2019

Keywords

05A15
33E05
Dumont differential system
Jacobi elliptic functions
context-free grammars
permutation statistics

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10.1007/s11425-016-9240-5

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author = "Ma, {Shi Mei} and Toufik Mansour and Wang, {David G.L.} and Yeh, {Yeong Nan}",

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AU - Wang, David G.L.

AU - Yeh, Yeong Nan

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Y1 - 2019/10/1

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KW - 33E05

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KW - Jacobi elliptic functions

KW - context-free grammars

KW - permutation statistics

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JO - Science China Mathematics

JF - Science China Mathematics

IS - 10

ER -

Several variants of the Dumont differential system and permutation statistics

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Keywords

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