Asymptotic results for uniform group drawing in the coupon collector’s problem

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 (Formula presented.) distinct coupons selected uniformly at random from a set of (Formula presented.) coupons. We focus on three regimes of the package size (Formula presented.) : (i) constant (Formula presented.), (ii) (Formula presented.) proportional to (Formula presented.), and (iii) (Formula presented.) “very close” to (Formula presented.). For each case, we provide precise asymptotic expressions for the expected collection time.