Coupons collecting with or without replacement, and with multipurpose coupons

TL;DR

This paper generalizes the Coupon-Collector Problem to include coupons with multiple purposes and introduces an efficient algorithm for counting specific transversals, enhancing understanding of complex coupon collection scenarios.

Contribution

It presents a novel generalization of the CCP involving multi-purpose coupons and develops an efficient algorithm for counting transversals in set systems.

Findings

Efficient algorithm for counting k-element transversals.

Generalization of CCP to multi-purpose coupons.

Uses basic probability theory for analysis.

Abstract

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 transversals of a set system.