The Open UniversitySkip to content
 

Maximum partial triple systems on 16 and 17 points

Demirkale, Fatih; Donovan, Diane and Grannell, Mike (2021). Maximum partial triple systems on 16 and 17 points. Utilitas Mathematica (In Press).

Google Scholar: Look up in Google Scholar

Abstract

It is shown that, up to isomorphism, there are 35,810,097 maximum partial triple systems on 17 points and 47,744,568 maximal partial triple systems on 16 points. It is also established that there are 157,151 non-isomorphic pairwise balanced designs, PBD(17,{3,5})s, having a single block of size 5. Structural properties of all these systems are determined, including their automorphism groups, and the numbers of Pasch configurations, mitres and Fano planes contained in them. The systems themselves are available from the authors at http://www.yildiz.edu.tr/~fatihd/MMPTS/.

Item Type: Journal Item
Copyright Holders: Utilitas Mathematica
Keywords: Maximum partial triple system; Steiner triple system; Pairwise balanced design; Pasch configuration; Mitre configuration.
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 53761
Depositing User: Mike Grannell
Date Deposited: 12 Mar 2018 09:52
Last Modified: 27 Jun 2018 07:44
URI: http://oro.open.ac.uk/id/eprint/53761
Share this page:

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU