Some new aspects of the coupon-collector's problem

Details Some new aspects of the coupon-collector's problem Some new aspects of the coupon-collector's problem

2003-04-16

arxiv.org/abs/math/0304229v1

Mathematics

Combinatorics

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Some new aspects of the coupon-collector's problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Some new aspects of the coupon-collector's problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some new aspects of the coupon-collector's problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-10472