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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.

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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 …
Noam D. Elkies's user avatar