The Probabilistic Pigeonhole Principle

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-06-23 DOI:10.1080/00029890.2023.2219174

Soumya Bhattacharya

引用次数: 0

Abstract

The pigeonhole principle states that if n pigeons are put into m < n pigeonholes, then at least two pigeons must be in the same hole. What happens if there are more pigeonholes than pigeons and the pigeons are placed in the pigeonholes randomly? For example, if each among 50 shades of grey are chosen at random from 256 possibilities, can one assert that there are at least two identical choices? Yes, almost surely one can! See Corollary 1. Theorem (Probabilistic Pigeonhole Principle). Given a positive integer m and p ∈ [0, 1), let n be an integer that is larger than or equal to

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概率鸽子洞原理

鸽子洞原理指出，如果将n只鸽子放入m < n个鸽子洞中，则至少有两只鸽子在同一个鸽子洞中。如果鸽子洞比鸽子多，鸽子被随机放置在鸽子洞里，会发生什么?例如，如果从256种可能性中随机选择50种灰度中的每一种，人们是否可以断言至少有两个相同的选择?是的，几乎可以肯定!参见推论1。定理(概率鸽子洞原理)。给定正整数m, p∈[0,1]，设n为大于等于的整数

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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