Sur le groupe d'interpolation

Sur la Classification et le Denombrement des Sous-groupes du Groupe Modulaire et de leurs Classes de Conjugaison

In this article we give a classification of the sub-groups in PSL(2,Z) and of the conjugacy classes of these sub-groups by the mean of an combinatorial invariant: some trivalent diagrams (dotted or not). We give explicit formulae enabling to count the number of isomorphism classes of these structures and of some of their variations, as function of the number of their arcs. Until now, the counting of non-dotted diagrams was an open problem, for it gives also the number of unrooted combinatorial maps, triangular or general respectively. The article ends with the description of a high performance…

$λ$-quiddit{é} 关于 $\mathbb{C}$ 的某些单生成子群

$λ$-quiddit{é} sur certains sous-groupes monog{è}nes de $\mathbb{C}$

本文在复数加法群的循环子群上研究 $λ$-quiddity，特别关注由 $\sqrt{k}$ 和 $i\sqrt{k}$ 生成的子群，延续考克斯特饰带研究中的问题。

关于模群生成元与 $λ$-quiddities 的计数元素

Éléments de comptage sur les générateurs du groupe modulaire et les $λ$-quiddités

本文旨在计算满足特定矩阵方程的正整数 $n$ 元组解的数量，其中矩阵 $M$ 取模群的生成元，并通过研究最后一个分量固定的 $λ$-quiddities 来实现这一计数。

Action of the symmetric groups on the homology of the hypertree posets

The set of hypertrees on $n$ vertices can be endowed with a poset structure. J. McCammond and J. Meier computed the dimension of the unique non zero homology group of the hypertree poset. We give another proof of their result and use the theory of species to determine the action of the symmetric group on this homology group, which is linked with the anti-cyclic structure of the $\operatorname{Prelie}$ operad. We also compute the action on the Whitney homology of the poset. ----- L'ensemble des hyperarbres à $n$ sommets peut être muni d'un ordre partiel. J. McCammond et J. Meier ont calculé la …