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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