Séminaire Lotharingien de Combinatoire, B32a (1994), 3 pp.

Jacques Désarménien

Distribution de l'indice majeur réduit sur les dérangements

Abstract. The number of derangements of n objects, denoted by d(n), satisfies the recurrence relation : d(n)=nd(n-1)+1 or nd(n-1)-1, depending on whether n is even or odd. We have proved in a previous paper how a combinatorial model different from the usual derangement model provided a simple proof of the forementioned recurrence. This model has been further exploited and embedded in the context of symmetric functions. It is also possible to obtain explicit formulas for the q-derangements and also to study the reduction of the mahonian statistics modulo n. In this paper we show how the notion of reduced major index yields a direct interpretation of the above formula.

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