A propos du choix du partenaire en aïkido : éléments d'algèbre et de combinatoire des appariements d'un ensemble fini

Mathématiques et sciences humaines. Mathematics and social sciences

Barbut, Marc¹  Duprez, Jean-Marie¹ 

关键词: aïkido;    configuration;    homogeneity;    pairing;    probabilities;    lattice;   

DOI  :  10.4000/msh.4083

学科分类：数学（综合）

来源: College de France * Ecole des Hautes Etudes en Sciences Sociales (E H E S S)

【 摘 要 】

The rules of the game named aïkido provide a particular occurrence of the following general problem: a finite set E(|E|= 2n) of persons is divided into k given classes (partition ∏); each person is allowed to choose freely a partner among the others; the result is a second partition of E, into n 2-subsets; we name it pairing. The sequence of the sizes of the classes of the cut (infimum) of ∏ and a pairing (in the partitions lattice of E) is called here a configuration. This paper studies the set of all possible configurations in the two elementary cases k = 2 and k = 3. For (k ≥ 4), some general properties are showed.

【 授权许可】

Unknown