Related papers: A Generalized Coupon Collector Problem
In this note we evaluate the expectation and variance of the waiting time to complete $m$ parallel collections of coupons, in the case of coupons which arrives independently, one by one and with equal probabilities.
A popular variant of the collector's problem is the following: Assume there are $N$ different types of coupons with equal occurring probabilities. There is one main collector who collects coupons. When she gets a "double," she gives it to…
A collector samples coupons with replacement from a pool containing $g$ \textit{uniform} groups of coupons, where "uniform group" means that all coupons in the group are equally likely to occur. For each $j = 1, \dots, g$ let $T_j$ be the…
To approximate the trajectories of a stochastic process by the solution of some differential equation is widely used in the fields of probability, computer science and combinatorics. In this paper, the convergence of coupon collecting…
In the coupon collector problem with $n$ items, the collector needs a random number of tries $T_n\simeq n\ln n$ to complete the collection. Also, after $nt$ tries, the collector has secured approximately a fraction…
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to…
We study how efficiently a $k$-element set $S\subseteq[n]$ can be learned from a uniform superposition $|S\rangle$ of its elements. One can think of $|S\rangle=\sum_{i\in S}|i\rangle/\sqrt{|S|}$ as the quantum version of a uniformly random…
The classic Coupon-Collector Problem (CCP) is generalized to the extent that each coupons serves certain "purposes". Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all $k$-element…
We address a conjecture of Schilling concerning the optimality of the uniform distribution in the generalized Coupon Collector's Problem (CCP) where, in each round, a subset (package) of $s$ coupons is drawn from a total of $n$ distinct…
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…
We study a labeled variant of the classical Coupon Collector Problem (CCP), recently introduced by Tan et al., where coupons arrive in groups and only the set of labels is revealed. The goal is to determine the expected number of group…
In this paper the coupon collector's problem with group drawings is studied. Assume there are $ n $ different coupons. At each time precisely $ s $ of the $ n $ coupons are drawn, where all choices are supposed to have equal probability.…
We study the two-player coupon-collector competition in which two independent collectors draw one coupon each per round from a set of $d$ equally likely coupon types. Myers and Wilf gave finite formulae for several two-player events and…
The double Dixie cup problem of D.J. Newman and L. Shepp is a well-known variant of the coupon collector problem, where the object of study is the number of coupons that a collector has to buy in order to complete m sets of all N existing…
We study the coupon collector with deterministic expiration: one coupon is drawn at each time, and each coupon remains active for exactly $M$ draws. Completion occurs when all $n$ coupon types are simultaneously active. Equivalently, the…
Despite the coupon collector's problem has simple probabilistic solution using inclusion/exclusion principle \cite{PolyaUrn}, starting from a particular type of recurrence differential equation it is used an analytic approach to recover…
We examine the negative occupancy distribution and the coupon-collector distribution, both of which arise as distributions relating to hitting times in the extended occupancy problem. These distributions constitute a full solution to a…
We prove that, in the coupon collector's problem, the point processes given by the times of $r$-th arrivals for coupons of each type, centered and normalized in a proper way, converge toward a non-homogeneous Poisson point process. This…
The Coupon Collector's Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no…
An {\it Omnibus Sequence} of length $n$ is one that has each possible "message" of length $k$ embedded in it as a subsequence. We study various properties of Omnibus Sequences in this paper, making connections, whenever possible, to the…