Nearly Kirkman triple systems of order 18 and Hanani triple systems of order 19

Colbourn, Charles J., Kaski, Petteri, Ostergard, Patric R. J., Pike, David A. and Pottonen, Olli (2011) Nearly Kirkman triple systems of order 18 and Hanani triple systems of order 19. Discrete Mathematics, 311 10-11: 827-834. doi:10.1016/j.disc.2011.02.005

Author Colbourn, Charles J.
Kaski, Petteri
Ostergard, Patric R. J.
Pike, David A.
Pottonen, Olli
Title Nearly Kirkman triple systems of order 18 and Hanani triple systems of order 19
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2011-06-06
Year available 2011
Sub-type Article (original research)
DOI 10.1016/j.disc.2011.02.005
Open Access Status Not Open Access
Volume 311
Issue 10-11
Start page 827
End page 834
Total pages 8
Place of publication Amsterdam, The Netherlands
Publisher Elsevier BV * North-Holland
Language eng
Subject 2607 Discrete Mathematics and Combinatorics
2614 Theoretical Computer Science
Abstract A Hanani triple system of order 6n+1, HATS(6n+1), is a decomposition of the complete graph K6n+1 into 3n sets of 2n disjoint triangles and one set of n disjoint triangles. A nearly Kirkman triple system of order 6n, NKTS(6n), is a decomposition of K6n-F into 3n-1 sets of 2n disjoint triangles; here F is a one-factor of K6n. The Hanani triple systems of order 6n+1 and the nearly Kirkman triple systems of order 6n can be classified using the classification of the Steiner triple systems of order 6n+1. This is carried out here for n=3: There are 3787983639 isomorphism classes of HATS(19)s and 25328 isomorphism classes of NKTS(18)s. Several properties of the classified systems are tabulated. In particular, seven of the NKTS(18)s have orthogonal resolutions, and five of the HATS(19)s admit a pair of resolutions in which the almost parallel classes are orthogonal.
Keyword Hanani triple system
Nearly Kirkman triple system
Resolvable design
Steiner triple system
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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