Publ. l'I.R.M.A., Strasbourg, 476/TS-29, 1991, 119 pages
Guo-Niu Han
Calcul Denertien
(Thèse de Doctorat, 1991)
Abstract.
This doctoral thesis consists of three parts. In the first part,
a bijection ("the third fundamental transformation") is
constructed which maps the pair of word statistics (exc,den)
(where "exc" denotes the number of excedances and "den" denotes
the Denert statistics) to the pair (des,maj) (where "des" denotes
the number of descents and "maj" denotes MacMahon's major index).
The second part contains a combinatorial study of the Kostka-Foulkes
polynomials, where, in particular, monotonicity results for these
polynomials are proven. The third part is devoted to certain functions
(originally introduced by Dominique Dumont)
which are enumerated by the Genocchi numbers. We define three
statistics on these functions and prove a strong symmetry property for
them.
-
0. Introduction
- 1. La statistique de Denert
- 1.1. Distribution Euler-mahonienne : une correspondence
- 1.2. Une nouvelle bijection pour la statistique de Denert
- 1.3. La troisième transformation fondamentale
- 2. Statistique sur les tableaux de Young
- 2.1. Croissance des polynômes de Kostka
- 2.2. Polynômes de Kostka-Foulkes : une étude statistique
- 3. Symétries trivariées sur les nombres de
Genocchi
- 4. Bibliographie
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