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Related papers: The Labeled Coupon Collector Problem

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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.

Probability · Mathematics 2016-09-15 Marco Ferrante , Alessia Tagliavini

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…

Combinatorics · Mathematics 2007-05-23 Amy N. Myers , Herbert S. Wilf

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…

Probability · Mathematics 2014-01-20 Marcel Wild , Svante Janson , Stephan Wagner , Dirk Laurie

We consider an extended variant of the classical coupon collector's problem with infinite number of collections. An arriving coupon is placed in the $r^{th}$ collection, $r\ge0$, if $r$ is the smallest index such that the corresponding…

Probability · Mathematics 2020-02-04 Andrii Ilienko

The embedding problem of Markov transition matrices into continuous-time Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the…

Probability · Mathematics 2026-01-27 Ellen Baake , Michael Baake

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

We consider a generalisation of the classical coupon collector problem. We define a super-coupon to be any $s$-subset of a universe of $n$ coupons. In each round, a random $r$-subset from the universe is drawn and all its $s$-subsets are…

Probability · Mathematics 2023-09-13 Siva Athreya , Satyaki Mukherjee , Soumendu Sundar Mukherjee

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 "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

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

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

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

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

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

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

This article explores the intersection of the Coupon Collector's Problem and the Orthogonal Matrix Factorization (OMF) problem. Specifically, we derive bounds on the minimum number of columns $p$ (in $\mathbf{X}$) required for the OMF…

Signal Processing · Electrical Eng. & Systems 2024-05-22 Anirudh Dash

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…

Probability · Mathematics 2022-01-11 Ben O'Neill

A basic question in the PAC model of learning is whether proper learning is harder than improper learning. In the classical case, there are examples of concept classes with VC dimension $d$ that have sample complexity $\Omega\left(\frac…

Quantum Physics · Physics 2024-03-07 Ashwin Nayak , Pulkit Sinha

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

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