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Putnam
1957 Putnam
B5
B5
Part of
1957 Putnam
Problems
(1)
increasing mapping on set power
Source: 16-th Hungary-Israel Binational Mathematical Competition 2005
3/29/2007
Let
f
f
f
be an increasing mapping from the family of subsets of a given finite set
H
H
H
into itself, i.e. such that for every
X
⊆
Y
⊆
H
X \subseteq Y\subseteq H
X
⊆
Y
⊆
H
we have
f
(
X
)
⊆
f
(
Y
)
⊆
H
.
f (X )\subseteq f (Y )\subseteq H .
f
(
X
)
⊆
f
(
Y
)
⊆
H
.
Prove that there exists a subset
H
0
H_{0}
H
0
of
H
H
H
such that
f
(
H
0
)
=
H
0
.
f (H_{0}) = H_{0}.
f
(
H
0
)
=
H
0
.
combinatorics unsolved
combinatorics