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

Department of Mathematics

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

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
State	Published - 1 Oct 2019

Bibliographical note

Publisher Copyright:
© 2018, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1007/s11425-016-9240-5

Cite this

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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 - Yeh, Yeong Nan

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ER -

Several variants of the Dumont differential system and permutation statistics

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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