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||About the choice of the partner in aïkido: elements of algebra and combinatorics of the pairing of a finite set
||BARBUT Marc, DUPREZ Jean-Marie
||Aïkido, Configuration, Homogeneity, Lattice, Pairing, Probability
||Combinatorics, Lattices, Probabilities, Recurrence equations, Social Psychology, Sociology
||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 Π); 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 Π 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.
||177, Spring 2007 |
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