MathDB
HMMT Team 2019/2: "Weird" bijections on N

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February 17, 2019
HMMTcombinatoricsPrinceton

Problem Statement

Let N={1,2,3,… }\mathbb{N} = \{1, 2, 3, \dots\} be the set of all positive integers, and let ff be a bijection from N\mathbb{N} to N\mathbb{N}. Must there exist some positive integer nn such that (f(1),f(2),…,f(n))(f(1), f(2), \dots, f(n)) is a permutation of (1,2,…,n)(1, 2, \dots, n)?
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