| proposed by | Francisco Azevedo fa@di.fct.unl.pt |
The ternary Steiner problem of order n consists of finding a set of n.(n-1)/6 triples of distinct integer elements in {1,…,n} such that any two triples have at most one common element. It is a hypergraph problem coming from combinatorial mathematics [Lueneburg 1989] where n modulo 6 has to be equal to 1 or 3 [Lindner and Rosa 1980]. One possible solution for n=7 is {{1, 2, 3}, {1, 4, 5}, {1, 6, 7}, {2, 4, 6}, {2, 5, 7}, {3, 4, 7}, {3, 5, 6}}. The solution contains 7*(7-1)/6 = 7 triples.
This is a particular case of the more general Steiner system.