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1998 IMC
4
IMC 1998 Problem 10
IMC 1998 Problem 10
Source: IMC 1998 Day 2 Problem 4
October 28, 2020
function
combinatorics
Problem Statement
Let
S
n
=
{
1
,
2
,
.
.
.
,
n
}
S_{n}=\{1,2,...,n\}
S
n
=
{
1
,
2
,
...
,
n
}
. How many functions
f
:
S
n
→
S
n
f:S_{n} \rightarrow S_{n}
f
:
S
n
→
S
n
satisfy
f
(
k
)
≤
f
(
k
+
1
)
f(k) \leq f(k+1)
f
(
k
)
≤
f
(
k
+
1
)
and
f
(
k
)
=
f
(
f
(
k
+
1
)
)
f(k)=f(f(k+1))
f
(
k
)
=
f
(
f
(
k
+
1
))
for
k
<
n
?
k <n?
k
<
n
?
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