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There exists f such that A and f(A) are disjoint

Source: IMO LongList 1982 - P42

May 16, 2011
functiongraph theorycombinatorics unsolvedcombinatorics

Problem Statement

Let F\mathfrak F be the family of all kk-element subsets of the set {1,2,…,2k+1}\{1, 2, \ldots, 2k + 1\}. Prove that there exists a bijective function f:F→Ff :\mathfrak F \to \mathfrak F such that for every A∈FA \in \mathfrak F, the sets AA and f(A)f(A) are disjoint.
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