A triple (x,y,z) cyclically contains the ordered pairs (x,y), (y,z), (z,x), and no others. A Mendelsohn triple system of order v, or MTS (v,λ), is a set V together with a collection B of ordered triples of distinct elements from V, such that |V|=v and each ordered pair (x,y)V×V with x≠y is cyclically contained in exactly λ ordered triples. By means of a computer search, we classify all Mendelsohn triple systems of order 13 with λ=1; there are 6 855 400 653 equivalence classes of such systems.
- Mendelsohn triple system
- automorphism group
- isomorph-free exhaustive generation
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics