Séminaire Lotharingien de Combinatoire, vol. 47, B47a, 2001, 20 pages.

Dominique Foata, Guo Niu Han, Bodo Lass

Les nombres hyperharmoniques et la fratrie du collectionneur de vignettes

Abstract. The traditional coupon collector's problem is extended to the case where the collector shares his harvest with his own phratry. He remains the only coupon provider, but gives his brothers the coupons that have already appeared in his picture-book. When his book is completed, the books of the other brothers have certain numbers of empty spots. On the average, how many? We bring an answer to this question and also derive the multivariable generating function for the random variables involved. The problem gives rise to the hyperharmonic numbers that are to be studied under various aspects, in particular as solutions of finite-difference equations.

foata@math.u-strasbg.fr, guoniu@math.u-strasbg.fr, lass@math.u-strasbg.fr

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