Sparse Steiner triple systems of order 21

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Abstract

A (Formula presented.) -configuration is a set of (Formula presented.) blocks on (Formula presented.) points. For Steiner triple systems, (Formula presented.) -configurations are of particular interest. The smallest nontrivial such configuration is the Pasch configuration, which is a (Formula presented.) -configuration. A Steiner triple system of order (Formula presented.), an STS (Formula presented.), is (Formula presented.) -sparse if it does not contain any (Formula presented.) -configuration for (Formula presented.). The existence problem for anti-Pasch Steiner triple systems has been solved, but these have been classified only up to order 19. In the current work, a computer-aided classification shows that there are 83,003,869 isomorphism classes of anti-Pasch STS(21)s. Exploration of the classified systems reveals that there are three 5-sparse STS(21)s but no 6-sparse STS(21)s. The anti-Pasch STS(21)s lead to 14 Kirkman triple systems, none of which is doubly resolvable.

Detaljer

Författare
  • Janne I. Kokkala
  • Patric R.J. Östergård
Enheter & grupper
Externa organisationer
  • University of Copenhagen
  • Aalto University
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematisk analys
  • Datavetenskap (datalogi)

Nyckelord

Originalspråkengelska
Sidor (från-till)75-83
Antal sidor9
TidskriftJournal of Combinatorial Designs
Volym29
Utgåva nummer2
Tidigt onlinedatum2020 nov 17
StatusPublished - 2021 feb
PublikationskategoriForskning
Peer review utfördJa