Séminaire Lotharingien de Combinatoire, 58 (2007), Article B58a

Dominique Foata, Guo-Niu Han

DECREASES AND DESCENTS IN WORDS

Abstract. The generating function for words by a multivariable statistic involving decrease, increase, descent and rise values is explicitly calculated by using the properties of the first fundamental transformation on words and the MacMahon Master Theorem in its noncommutative version. Applications to the calculation of factorial generating functions for the symmetric groups are also given.

foata at math dot u-strasbg dot fr, guoniu at math dot u-strasbg dot fr

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