Computing non-isomorphic 2-factorizations of K11 of type E2F3

  1. Generation -- we started with 6 non-isomorphic disjoint pairs of  E-type 2-factors and generated all F-type 2-factors disjoint with a given start:
    start 0 -- we generated 214 2-factors
    start 1 -- we generated 213 2-factors
    start 2 -- we generated 205 2-factors
    start 3 -- we generated 203 2-factors
    start 4 -- we generated 210 2-factors
    start 5 -- we generated 197 2-factors
  2. For each start we computed all systems of three disjoint F-type 2-factors using the sets generated in the previous step.
    start 0 -- we generated no disjoint system
    start 1 -- we generated 5 disjoint systems
    start 2 -- we generated no disjoint system
    start 3 -- we generated 2 disjoint systems
    start 4 -- we generated 2 disjoint systems
    start 5 -- we generated no disjoint system
  3. The sets obtained in the previous step were partitioned into classes of isomorphisms (buckets).
    start 1 --  we got 4 buckets
    start 3 --  we got 2 buckets
    start 4 --  we got 2 buckets
  4. From each bucket obtained in the previous step we chose a single representative, i.e. 8 systems
  5. For each system, using the same program for finding isomorphisms, the group of automorphisms was computed obtaining in the group sizes.