Abstract
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 language | English |
---|---|
Pages (from-to) | 1-11 |
Number of pages | 11 |
Journal | Journal of Combinatorial Designs |
Volume | 22 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2014 |
Keywords
- Mendelsohn triple system
- automorphism group
- isomorph-free exhaustive generation
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics