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Keywords:

  • automorphism group;
  • Mendelsohn triple system;
  • isomorph-free exhaustive generation

Abstract

A triple inline image cyclically contains the ordered pairs inline image, inline image, inline image, and no others. A Mendelsohn triple system of order v, or inline image, is a set V together with a collection inline image of ordered triples of distinct elements from V, such that inline image and each ordered pair inline image with inline image is cyclically contained in exactly λ ordered triples. By means of a computer search, we classify all Mendelsohn triple systems of order 13 with inline image; there are 6 855 400 653 equivalence classes of such systems.