MathDB

{A \choose r} denote the family of all r-element subsets of A, function

Source: Romania IMO TST 1989 1.4

February 17, 2020

functioncombinatorics

Problem Statement

Let

r,n

be positive integers. For a set

A

, let

{A \choose r}

denote the family of all

r

-element subsets of

A

. Prove that if

A

is infinite and

f : {A \choose r} \to {1,2,...,n}

is any function, then there exists an infinite subset

B

A

such that

f(X) = f(Y)

for all

X,Y \in {B \choose r}