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We consider here the maximum number of Slater orders that a tournament T with sigma(T) = 1 can get, where sigma(T) is a parameter defined from the scores of T. We compute this maximum number, which is about 2n/2, if n denotes the number of vertices. We depict also the tournaments T with sigma(T) = 1 maximizing the number of Slater orders and we show that the tournaments are not strongly connected for n even.

Nombre maximum d'ordres de Slater des tournois T vérifiant sigma(T) = 1