Enumeration of steiner triple systems with subsystems

Petteri Kaski, Patric R J östergård, Alexandru Popa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A Steiner triple system of order v, an STS(v), is a set of 3-element subsets, called blocks, of a v-element set of points, such that every pair of distinct points occurs in exactly one block. A subsystem of order w in an STS(v), a sub-STS(w), is a subset of blocks that forms an STS(w). Constructive and nonconstructive techniques for enumerating up to isomorphism the STS(v) that admit at least one sub-STS(w) are presented here for general parameters v and w. The techniques are further applied to show that the number of isomorphism classes of STS(21)s with at least one sub-STS(9) is 12661527336 and of STS(27)s with a sub-STS(13) is 1356574942538935943268083236.

Original languageEnglish
Pages (from-to)3051-3067
Number of pages17
JournalMathematics of Computation
Volume84
Issue number296
DOIs
Publication statusPublished - 2015

Keywords

  • Classification
  • Enumeration
  • Steiner triple system
  • Subsystem

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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  • Cite this

    Kaski, P., östergård, P. R. J., & Popa, A. (2015). Enumeration of steiner triple systems with subsystems. Mathematics of Computation, 84(296), 3051-3067. https://doi.org/10.1090/mcom/2945