@article{f3b69472373547409bee292ef05be74d,
title = "Several variants of the Dumont differential system and permutation statistics",
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.",
keywords = "05A15, 33E05, Dumont differential system, Jacobi elliptic functions, context-free grammars, permutation statistics",
author = "Ma, {Shi Mei} and Toufik Mansour and Wang, {David G.L.} and Yeh, {Yeong Nan}",
note = "Publisher Copyright: {\textcopyright} 2018, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2019",
month = oct,
day = "1",
doi = "10.1007/s11425-016-9240-5",
language = "English",
volume = "62",
pages = "2033--2052",
journal = "Science China Mathematics",
issn = "1674-7283",
publisher = "Science Press",
number = "10",
}