Asymptotic results for uniform group drawing in the coupon collector’s problem
Abstract
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 selected uniformly at random from a set of n coupons. We focus on three regimes of the package size s: (i) constant s, (ii) s proportional to n, and (iii) s “very close” to n. For each case, we provide precise asymptotic expressions for the expected collection time.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometric Analysis and Curvature Flows
Point processes and geometric inequalities
Publication details
- Journal / source
- Stochastic Models
- Publisher
- Informa UK Limited
- Volume
- 42
- Issue
- 3
- Pages
- 455–468
- Publication date
- 18 May 2026
- Language
- EN