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Ross 2010): There is one main collector who collects coupons. Assume there are $N$ different types of coupons with, in general, unequal occurring probabilities. When the main collector gets a \"double\", she gives it to her older brother; when this brother gets a \"double\", he gives it to the next brother, and so on. 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Doumas, Vassilis G. Papanicolaou","submitted_at":"2014-12-14T12:20:20Z","abstract_excerpt":"The following variant of the collector's problem has attracted considerable attention relatively recently (see, e.g., N. Pintacuda 1980, D. Foata H. Guo-Niu and B. Lass 2001, D. Foata and D. Zeilberger 2003, I. Adler, S. Oren and S. Ross 2003, and S. Ross 2010): There is one main collector who collects coupons. Assume there are $N$ different types of coupons with, in general, unequal occurring probabilities. When the main collector gets a \"double\", she gives it to her older brother; when this brother gets a \"double\", he gives it to the next brother, and so on. 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