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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
16
votes
Accepted
Intersecting 4-sets
The conjectured maximum of $N = \binom{\lfloor n/2\rfloor}{2}$
is correct except for $n=7$, when the maximum is $7$, and
$8 \leq n \leq 11$, when the maximum is $14$. The maximal
configuration is uni …