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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 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

Computer-based tests with randomly generated questions allow a large number of different tests to be generated. Given a fixed number of alternatives for each question, the number of tests that need to be generated before all possible…

Probability · Mathematics 2010-03-04 Charles M. Goldie , Rosie Cornish , Carol L. Robinson

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

Testing probabilistic programs is non-trivial due to their stochastic nature. Given an input, the program may produce different outcomes depending on the underlying stochastic choices in the program. This means testing the expected outcomes…

Software Engineering · Computer Science 2025-09-03 Katrine Christensen , Mahsa Varshosaz , Raúl Pardo

We extend the Coupon Collector's Problem (CCP) and present a novel generalized model, referred as the k-LCCP problem, where one is interested in recovering a bipartite graph with a perfect matching, which represents the coupons and their…

Discrete Mathematics · Computer Science 2025-02-06 Shoham Shimon Berrebi , Eitan Yaakobi , Zohar Yakhini , Daniella Bar-Lev

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

Empirical studies of scientific discovery---so-called Eurekometrics---have indicated that the output of exploration proceeds as a logistic growth curve. Although logistic functions are prevalent in explaining population growth that is…

Applications · Statistics 2017-08-15 Aditya Vempaty , Lav R. Varshney , Pramod K. Varshney

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

The solution of the classical Coupon Collector's Problem is based on the assumptions that all stickers are independently and uniformly distributed. We can prove statistically as well as analytically that in particular the assumption of…

Probability · Mathematics 2016-03-10 Niklas Braband , Sonja Braband , Malte Braband

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

A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the…

Combinatorics · Mathematics 2010-09-21 Giuseppe Scollo

This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The problem is to…

Probability · Mathematics 2016-03-18 Amirhossein Taghvaei , Prashant G. Mehta

The article explores the asymptotic behavior of the expected number of drawings in the Coupon Collector's Problem with group-drawing under the uniform distribution. In this variant, each draw consists of a package of $s$ distinct coupons…

Probability · Mathematics 2026-05-11 Daniel Berend , Tomer Sher

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

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

We propose an approach to analyze the asymptotic behavior of P\'olya urns based on the contraction method. For this, a new combinatorial discrete time embedding of the evolution of the urn into random rooted trees is developed. A…

Probability · Mathematics 2019-02-20 Margarete Knape , Ralph Neininger

This paper introduces and analyzes a particular class of Polya urns: balls are of two colors, can only be added (the urns are said to be additive) and at every step the same constant number of balls is added, thus only the color…

Combinatorics · Mathematics 2012-03-26 Basile Morcrette

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