Kirkman triple systems with subsystems

Janne I. Kokkala, Patric R.J. Östergård

Research output: Contribution to journalArticleScientificpeer-review

Abstract

A Steiner triple system of order v, STS(v), together with a resolution of its blocks is called a Kirkman triple system of order v, KTS(v). A KTS(v) exists if and only if v≡3(mod6). The smallest order for which the KTS(v) have not been classified is v=21, which is also the smallest order for which the existence of a doubly resolvable STS(v) is open. Here, KTS(21) with STS(7) and STS(9) subsystems are classified, leading to more than 13 million KTS(21). In this process, systems missing from an earlier classification of KTS(21) with nontrivial automorphisms are encountered, so such a classification is redone.

Original languageEnglish
Article number111960
JournalDiscrete Mathematics
Volume343
Issue number9
DOIs
Publication statusPublished - Sep 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Automorphism group
  • Doubly resolvable
  • Kirkman triple system
  • Resolution
  • Steiner triple system
  • Subsystem

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  • Projects

    Construction and Classification of Discrete Mathematic Structures

    Kokkala, J., Laaksonen, A., Heinlein, D., Ganzhinov, M., Östergård, P. & Szollosi, F.

    01/09/201524/09/2019

    Project: Academy of Finland: Other research funding

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