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Some kind of functional equation

Source: Science ON 2021 grade X/2

March 8, 2021

algebracombinatoricsfunctional equation

Problem Statement

Let

X

be a set with

n\ge 2

elements. Define

\mathcal{P}(X)

to be the set of all subsets of

X

. Find the number of functions

f:\mathcal{P}(X)\mapsto \mathcal{P}(X)

such that

|f(A)\cap f(B)|=|A\cap B|

whenever

A

and

B

are two distinct subsets of

X

.
(Sergiu Novac)

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