Steiner Triple Systems with an Involution

Alan Hartman, Dean G. Hoffman

Research output: Contribution to journalArticlepeer-review


Let π be a permutation of the set {1, 2,..., υ} having f< υ fixed points and (υ — f)/2 disjoint transpositions. We investigate the existence of Steiner triple systems admitting π as an auto-morphism. When f = 1 such a system is known as a reverse Steiner triple system and it is known that reverse Steiner triple systems exist if and only if υ ≡ 1, 3, 9 or 19 (mod 24). In this paper we show that a Steiner triple system admitting π as an automorphism, and f > 1 exists if and only if υ ≡ 1 or 3(mod 6), f ≡ 1 or 3(mod 6), and either (υ — f ≡ 0(mod 4), and υ ⩾ 2f + 1) or (υ — f ≡ 2 (mod 4), and υ ⩾ 3f).

Original languageEnglish
Pages (from-to)371-378
Number of pages8
JournalEuropean Journal of Combinatorics
Issue number4
StatePublished - 1987
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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