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Related papers: New results on a generalized coupon collector prob…

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We consider the following variant of the classic collector's problem: The family of coupon probabilities is the mixing of two subfamilies one of which is the \textit{uniform} family, while the other belongs to the well known \textit{Zipf…

Probability · Mathematics 2019-04-23 Aristides V. Doumas , Vassilis G. Papanicolaou

Based upon inequalities on Subset Probabilities, proofs of several conjectures on the Generalized Coupon Collector Problem (i.e. CCP with unequal popularity) are presented. Then we derive a very simple asymptotic relation between the…

Discrete Mathematics · Computer Science 2017-06-19 Christian Berthet

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…

Probability · Mathematics 2025-10-28 Dina Barak-Pelleg , Daniel Berend

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…

Probability · Mathematics 2020-05-13 Vassilis G. Papanicolaou , Aristides V. Doumas

Motivated by applications in bioinformatics, we consider the word collector problem, i.e. the expected number of calls to a random weighted generator of words of length $n$ before the full collection is obtained. The originality of this…

Discrete Mathematics · Computer Science 2012-04-18 Jérémie Du Boisberranger , Danièle Gardy , Yann Ponty

The "double Dixie cup problem" of D.J. Newman and L. Shepp (1960) is a well-known variant of the coupon collector's problem, where the object of study is the number $T_{m}(N)$ of coupons that a collector has to buy in order to complete $m$…

Probability · Mathematics 2015-11-06 Aristides V. Doumas , Vassilis G. Papanicolaou

Motivated by a problem in the theory of randomized search heuristics, we give a very precise analysis for the coupon collector problem where the collector starts with a random set of coupons (chosen uniformly from all sets). We show that…

Discrete Mathematics · Computer Science 2017-08-01 Benjamin Doerr , Carola Doerr

This paper is about the Coupon collector's problem. There are some coupons, or baseball cards, or other plastic knick-knacks that are put into bags of chips or under soda bottles, etc. A collector starts collecting these trinkets and wants…

Probability · Mathematics 2020-03-11 Rohit Pandey

The paper introduces a modified version of the classical Coupon Collector's Problem entailing exchanges and cooperation between multiple players. Results of the development show that, within a proper Markov framework, the complexity of the…

Discrete Mathematics · Computer Science 2009-12-15 R. Rovatti , C. Passerini , G. Mazzini

To reduce computational complexity and delay in randomized network coded content distribution (and for some other practical reasons), coding is not performed simultaneously over all content blocks but over much smaller subsets known as…

Information Theory · Computer Science 2010-06-04 Yao Li , Emina Soljanin , Predrag Spasojevic

For a given absorbing Markov chain $X^*$ on a finite state space, a chain $X$ is a sharp antidual of $X^*$ if the fastest strong stationary time of $X$ is equal, in distribution, to the absorption time of $X^*$. In this paper we show a…

Probability · Mathematics 2019-03-04 Paweł Lorek

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…

Probability · Mathematics 2014-12-16 Aristides V. Doumas , Vassilis G. Papanicolaou

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…

Probability · Mathematics 2025-10-31 Aristides V. Doumas

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…

Combinatorics · Mathematics 2023-02-22 Tipaluck Krityakierne , Thotsaporn Aek Thanatipanonda

We initiate the study of the Careless Coupon Collector's Problem (CCCP), a novel variation of the classical coupon collector, that we envision as a model for information systems such as web crawlers, dynamic caches, and fault-resilient…

Discrete Mathematics · Computer Science 2026-02-25 Emilio Cruciani , Aditi Dudeja

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…

Probability · Mathematics 2019-09-16 Andrii Ilienko

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…

Probability · Mathematics 2018-11-13 Aristides V. Doumas , Vassilis G. Papanicolaou

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…

Probability · Mathematics 2019-12-06 Anshui Li , Yong Chen

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…

Probability · Mathematics 2016-09-06 Andrea Monsellato

Let $V$ be an $n$-set, and let $X$ be a random variable taking values in the powerset of $V$. Suppose we are given a sequence of random coupons $X_1, X_2, \ldots $, where the $X_i$ are independent random variables with distribution given by…

Probability · Mathematics 2016-01-19 Victor Falgas-Ravry , Joel Larsson , Klas Markström