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Miklós Schweitzer
1968 Miklós Schweitzer
8
Miklos Schweitzer 1968_8
Miklos Schweitzer 1968_8
Source:
October 8, 2008
combinatorics proposed
combinatorics
Problem Statement
Let
n
n
n
and
k
k
k
be given natural numbers, and let
A
A
A
be a set such that
∣
A
∣
≤
n
(
n
+
1
)
k
+
1
.
|A| \leq \frac{n(n+1)}{k+1}.
∣
A
∣
≤
k
+
1
n
(
n
+
1
)
.
For
i
=
1
,
2
,
.
.
.
,
n
+
1
i=1,2,...,n+1
i
=
1
,
2
,
...
,
n
+
1
, let
A
i
A_i
A
i
be sets of size
n
n
n
such that
∣
A
i
∩
A
j
∣
≤
k
(
i
≠
j
)
,
|A_i \cap A_j| \leq k \;(i \not=j)\ ,
∣
A
i
∩
A
j
∣
≤
k
(
i
=
j
)
,
A
=
⋃
i
=
1
n
+
1
A
i
.
A= \bigcup_{i=1}^{n+1} A_i.
A
=
i
=
1
⋃
n
+
1
A
i
.
Determine the cardinality of
A
A
A
. K. Corradi
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