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IMO Longlists
1982 IMO Longlists
42
42
Part of
1982 IMO Longlists
Problems
(1)
There exists f such that A and f(A) are disjoint
Source: IMO LongList 1982 - P42
5/16/2011
Let
F
\mathfrak F
F
be the family of all
k
k
k
-element subsets of the set
{
1
,
2
,
…
,
2
k
+
1
}
\{1, 2, \ldots, 2k + 1\}
{
1
,
2
,
…
,
2
k
+
1
}
. Prove that there exists a bijective function
f
:
F
→
F
f :\mathfrak F \to \mathfrak F
f
:
F
→
F
such that for every
A
∈
F
A \in \mathfrak F
A
∈
F
, the sets
A
A
A
and
f
(
A
)
f(A)
f
(
A
)
are disjoint.
function
graph theory
combinatorics unsolved
combinatorics