Several variants of the Dumont differential system and permutation statistics
Combinatorics
2018-01-22 v2
Abstract
The Dumont differential system on the Jacobi elliptic functions was introduced by Dumont (Math Comp, 1979, 33: 1293--1297) 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
Cite
@article{arxiv.1403.0233,
title = {Several variants of the Dumont differential system and permutation statistics},
author = {Shi-Mei Ma and Toufik Mansour and David G. L. Wang and Yeong-Nan Yeh},
journal= {arXiv preprint arXiv:1403.0233},
year = {2018}
}
Comments
19 pages, to appear in Science China Mathematics