Several variants of the Dumont differential system and permutation statistics
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 o...
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| Veröffentlicht in: | Science China. Mathematics 2019-10, Vol.62 (10), p.2033-2052 |
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| container_title | Science China. Mathematics |
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| creator | Ma, Shi-Mei Mansour, Toufik Wang, David G. L. Yeh, Yeong-Nan |
| description | 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. |
| doi_str_mv | 10.1007/s11425-016-9240-5 |
| format | Article |
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| subjects | Applications of Mathematics Differential equations Elliptic functions Mathematical analysis Mathematics Mathematics and Statistics Permutations |
| title | Several variants of the Dumont differential system and permutation statistics |
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