On Conjectures concerning the Labeled Coupon Collector Problem

TL;DR

This paper investigates a labeled variant of the Coupon Collector Problem where coupons arrive in groups, proving two conjectures for the case where groups consist of pairs, and analyzing the expected number of draws needed.

Contribution

It provides rigorous proofs for two conjectures related to the labeled CCP with pair groups, advancing understanding of this problem variant.

Findings

Proved two conjectures for the case of pair groups in labeled CCP.

Derived bounds on the expected number of group drawings.

Enhanced theoretical understanding of the labeled coupon collection process.

Abstract

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 drawings required to uniquely identify the labeling of all coupons. We focus on the case where groups consist of pairs ($k=2$), and provide rigorous proofs for two conjectures posed by Tan et al.