Computing non-isomorphic 2-factorizations of K11 of type E3F2

  1. Generation -- we started with 15 non-isomorphic disjoint pairs of  F-type 2-factors and generated all E-type 2-factors disjoint with a given start:
    start 0 -- we generated 240 2-factors
    start 1 -- we generated 236 2-factors
    start 2 -- we generated 212 2-factors
    start 3 -- we generated 217 2-factors
    start 4 -- we generated 192 2-factors
    start 5 -- we generated 212 2-factors
    start 6 -- we generated 224 2-factors
    start 7 -- we generated 222 2-factors
    start 8 -- we generated 192 2-factors
    start 9 -- we generated 192 2-factors
    start 10 -- we generated 228 2-factors
    start 11 -- we generated 192 2-factors
    start 12 -- we generated 192 2-factors
    start 13 -- we generated 168 2-factors
    start 14 -- we generated 196 2-factors
  2. For each start we computed all systems of three disjoint E-type 2-factors using the sets generated in the previous step.
    start 0 -- we generated 12 disjoint systems
    start 1 -- we generated 2 disjoint systems
    start 2 -- we generated no disjoint system
    start 3 -- we generated no disjoint system
    start 4 -- we generated no disjoint systems
    start 5 -- we generated no disjoint system
    start 6 -- we generated no disjoint system
    start 7 -- we generated 2 disjoint systems
    start 8 -- we generated no disjoint system
    start 9 -- we generated no disjoint system
    start 10 -- we generated no disjoint system
    start 11 -- we generated no disjoint system
    start 12 -- we generated no disjoint system
    start 13 -- we generated no disjoint system
    start 14 -- we generated no disjoint system
  3. The sets obtained in the previous step were partitioned into classes of isomorphisms, referred to as "buckets".
    start 0 --  we got 2 buckets
    start 1 --  we got 1 bucket
    start 7 --  we got 1 bucket
  4. From each bucket obtained in the previous step we chose a single representative, i.e. 4 systems
  5. For each system, using the same program for finding isomorphisms, the group of automorphisms was computed obtaining in the group sizes.