MathDB
Stable Permutation

Source: Iran 3rd round 2009 - final exam problem 2

January 2, 2015
combinatorics unsolvedcombinatorics

Problem Statement

Permutation π\pi of {1,…,n}\{1,\dots,n\} is called stable if the set {π(k)−k∣k=1,…,n}\{\pi (k)-k|k=1,\dots,n\} is consisted of exactly two different elements. Prove that the number of stable permutation of {1,…,n}\{1,\dots,n\} equals to σ(n)−τ(n)\sigma (n)-\tau (n) in which σ(n)\sigma (n) is the sum of positive divisors of nn and τ(n)\tau (n) is the number of positive divisors of nn.
Time allowed for this problem was 75 minutes.
Back to ProblemsView on AoPS