The mendelsohn triple systems of order 13

Mahdad Khatirinejad, Patric R.J. Östergård, Alexandru Popa

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Combinatorial Designs
Issue number1
Publication statusPublished - Jan 2014


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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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