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We consider a generalisation of the classical coupon collector's problem, in which at each time step a collector either receives a new copy of a randomly chosen coupon, or loses all their previously collected copies of that coupon. We…

Probability · Mathematics 2026-05-15 Luke J. Attrill , Timothy M. Garoni

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…

Discrete Mathematics · Computer Science 2017-03-07 Christian Berthet

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

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 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

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

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

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

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

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

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

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

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…

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

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…

History and Overview · Mathematics 2021-08-06 Niklas Braband , Sonja Braband , Malte Braband

The coupon collector is a prototypical model for evaluating the number of samples for identifying a set. By superposing all elements in the set as a pure quantum state, a quantum version of the coupon collector aims to learn the state,…

Quantum Physics · Physics 2024-06-18 Jing-Peng Zhang , Min-Quan He , Dan-Bo Zhang

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 focuses on the Coupon Collector's Problem with replacement (limited purchasing of missing stickers) and swapping. We have simulated combined strategies and found new results, which we were able to prove for a particular case. The…

Probability · Mathematics 2016-06-07 Niklas Braband , Sonja Braband , Malte Braband

This paper introduces an extension to the Orienteering Problem (OP), called Clustered Orienteering Problem with Subgroups (COPS). In this variant, nodes are arranged into subgroups, and the subgroups are organized into clusters. A reward is…

Artificial Intelligence · Computer Science 2023-12-29 Luciano E. Almeida , Douglas G. Macharet