论文标题
最慢的优惠券收藏家的问题
The slowest coupon collector's problem
论文作者
论文摘要
在古典优惠券收藏家的问题中，每盒早餐谷物都包含一个来自n个不同优惠券的优惠券，每个优惠券都可能出现。目标是找到玩家需要购买的预期盒子数量才能完成整个系列。在这项工作中，我们将经典问题扩展到了彼此竞争的K玩家，成为第一个收集整个收藏品的人。我们发现最慢，最快的玩家完成比赛所需的盒子数量。特定玩家是最慢或最快的球员的几率也将被触及。将从可拖动的代数技术以及观点的概率中讨论解决方案。
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to purchase to complete the whole collection. In this work, we extend the classical problem to k players who compete with one another to be the first to collect the whole collection. We find the expected numbers of boxes required for the slowest and fastest players to finish the game. The odds of a particular player being the slowest or fastest player will also be touched upon. The solutions will be discussed from both the tractable algebraic techniques as well as the probability point of views.
