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 - 2014 |
| Externally published | Yes |
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Keywords
- automorphism group
- isomorph-free exhaustive generation
- Mendelsohn triple system
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
Cite this
The mendelsohn triple systems of order 13. / Khatirinejad, Mahdad; Östergård, Patric R J; Popa, Alexandru.
In: Journal of Combinatorial Designs, Vol. 22, No. 1, 2014, p. 1-11.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The mendelsohn triple systems of order 13
AU - Khatirinejad, Mahdad
AU - Östergård, Patric R J
AU - Popa, Alexandru
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - automorphism group
KW - isomorph-free exhaustive generation
KW - Mendelsohn triple system
UR - http://www.scopus.com/inward/record.url?scp=84886952008&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84886952008&partnerID=8YFLogxK
U2 - 10.1002/jcd.21364
DO - 10.1002/jcd.21364
M3 - Article
VL - 22
SP - 1
EP - 11
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
SN - 1063-8539
IS - 1
ER -