(9,4,3)

Abstract

One combinatorial design that has particularly interested me is (9,4,3). With only nine numbers, and only 36 pairs of numbers, the system is small enough that one should be able to see how it works, and since by definition each pair occurs three times in three different blocks of four, all that is necessary is to write out the 36 pairs and connect each pair with the three other pairs that form one of the 18 blocks of the system. I could imagine all these three-armed pairs holding hands with one another in lovely triangular lattices, and since the Handbook of Combinatorial Design gives 11 completely different solutions to work with, I was sure that clearly spaced drawings would allow us to look inside each system and see how it all connects. I could imagine 11 drawings, all different, and all containing lovely symmetries.