I'm trying to figure out some simple bounds for the coupon collector problem with non-uniform coupon distribution in the best and worst case. I suspect the best case is uniform distribution with n log n coupons. What is it for worst case distribution?
Paper below looks relevant, but the setting is more general and I'm not sure how to get a simpler expression out of Theorem 3.1
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i2p33/pdf