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4
Combinatorics involving functions.
Combinatorics involving functions.
Source:
March 1, 2017
combinatorics
function
inequalities
Problem Statement
Let
n
n
n
be an integer bigger than
0
0
0
. Let
A
=
(
a
1
,
a
2
,
.
.
.
,
a
n
)
\mathbb{A}= ( a_1,a_2,...,a_n )
A
=
(
a
1
,
a
2
,
...
,
a
n
)
be a set of real numbers. Find the number of functions
f
:
A
→
A
f:A \rightarrow A
f
:
A
→
A
such that
f
(
f
(
x
)
)
−
f
(
f
(
y
)
)
≥
x
−
y
f(f(x))-f(f(y)) \ge x-y
f
(
f
(
x
))
−
f
(
f
(
y
))
≥
x
−
y
for any
x
,
y
∈
A
x,y \in \mathbb{A}
x
,
y
∈
A
, with
x
>
y
x>y
x
>
y
.
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