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find number of functions...

Source: Moldova TST Problem 4, day 3

March 31, 2015

functioncombinatorics

Problem Statement

Let

n

and

k

be positive integers, and let be the sets

X=\{1,2,3,...,n\}

and

Y=\{1,2,3,...,k\}

. Let

P

be the set of all the subsets of the set

X

. Find the number of functions

f: P \to Y

that satisfy

f(A \cap B)=\min(f(A),f(B))

for all

A,B \in P

.

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