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From: TCL on 10 May 2010 09:48
On May 9, 1:08 pm, TCL <tl...(a)cox.net> wrote:
> Characterize numbers a,b,c,d,e such that there exist five
> sets A_i, i=1,..,5 satisfying
>
> |A_i|=a for all i;
>
> |A_i \cap A_j|=b, for all i=/ j;
>
> |A_i \cap A_j \cap A_k|=c for all distinct i,j,k
>
> and so on.
>
> Of course two neccessary conditions on these numbers are that
>
> 5a-10b+10c-5d+e must be positive, and that a,b,c,d,e must be
>
> nonincreasing.
>
> (Here |A| denotes the cardinality of A.)

Some of my previous conditions are redundant (derivable from others).
My final conclusion is:
a,b,c,d,e are such numbers if and only if they are nonnegative and

d-e >= 0
c-2d+e >= 0
b-3c+3d-e >= 0
a-4b+6c-4d+e >= 0

TCL
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