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Some new aspects of the coupon collector’s problem (2004)
| Content Provider | CiteSeerX |
|---|---|
| Author | Herbert Wilf, S. Myers, Amy N. |
| Abstract | Abstract. We extend the classical coupon collector’s problem to one in which two collectors are simultaneously and independently seeking collections of d coupons. We find, in finite terms, the probability that the two collectors finish at the same trial, and we find, using the methods of Gessel– Viennot, the probability that the game has the following “ballot-like ” character: the two collectors are tied with each other for some initial number of steps, and after that the player who first gains the lead remains ahead throughout the game. As a by-product we obtain the evaluation in finite terms of certain infinite series whose coefficients are powers and products of Stirling numbers of the second kind. We study the variant of the original coupon collector’s problem in which a single collector wants to obtain at least h copies of each coupon. Here we give a simpler derivation of results of Newman and Shepp and extend those results. Finally we obtain the distribution of the number of coupons that have been obtained exactly once (“singletons”) at the conclusion of a successful coupon collecting sequence. Key words. coupon, Stirling number, lattice path AMS subject classification. 05-02 |
| File Format | |
| Journal | SIAM J. Discret. Math |
| Publisher Date | 2004-01-01 |
| Access Restriction | Open |
| Subject Keyword | Simpler Derivation Successful Coupon Original Coupon Collector Problem Classical Coupon Collector Problem Lattice Path Am Subject Classification Following Ballot-like Character Single Collector Coupon Collector Problem Certain Infinite Series Initial Number Gessel Viennot Finite Term |
| Content Type | Text |
| Resource Type | Article |
