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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.
8
votes
Intersecting 4-sets
Here's 14 sets on 8 points:
{ 2, 5, 7, 8 },
{ 2, 3, 6, 7 },
{ 2, 3, 4, 5 },
{ 2, 4, 6, 8 },
{ 1, 2, 4, 7 },
{ 1, 2, 3, 8 },
{ 3, 5, 6, 8 },
{ 1, 2, 5, 6 },
{ 1, 3, 5, 7 },
{ 1, 4, 5, 8 },
{ 3, 4, 7, …
7
votes
Accepted
Is the domination number of a combinatorial design determined by the design parameters?
Well, interestingly enough, all the 80 Steiner triple systems on 15 points have minimum dominating sets of size 10 - there is more tradeoff between the points/blocks than I first recognised.
But if w …