Kirkman triple systems of order 21 with nontrivial automorphism group

Myra B. Cohen, Charles J. Colbourn, Lee A. Ives, Alan C.H. Ling

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphism group. None of these is doubly resolvable. Four are quadrilateral-free, providing the first examples of such a KTS(21).

Original languageEnglish (US)
Pages (from-to)873-881
Number of pages9
JournalMathematics of Computation
Volume71
Issue number238
DOIs
StatePublished - Jan 1 2002
Externally publishedYes

Keywords

  • Constructive enumeration
  • Doubly resolvable design
  • Kirkman triple system
  • Steiner triple system

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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