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On Von Schelling Formula for the Generalized Coupon Collector Problem (1703.01886v1)
Published 6 Mar 2017 in cs.DM
Abstract: This paper gives an algebraic proof of the correctness of Von Schelling formula for the probability of the coupon collector problem waiting time for non-uniform distributions and partial collections. It introduces a theorem on sums of powers of subset probabilities which to our knowledge is new. A set of binomial coefficients is used as a basis for decomposition of these sums of powers.