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. Dans-le-sixième, . Dernier-chapitre-de-cette-thèse-;-bessiere, . Hebrard, . Hnich, . Kiziltan et al., ont développé deux nouvelles contraintes globales, range et roots , qui peuvent être utilisées pour spécifier de nombreuses contraintes de cardinalité. En d'autres termes, pour presque chaque contrainte de cardinalité, il existe un modèle équivalent utilisant uniquement les contraintes range et roots (et quelques contraintes arithmétiques). Nous montrons comment utiliser les décompositions range et roots pour dénombrer les solutions. Plus précisément, nous développons une approche probabiliste, Nous cardinalité initiales, 2009.