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(F, 2)—Rotational Steiner Triple Systems

  • Zhike Jiang
Part of the Mathematics and Its Applications book series (MAIA, volume 329)

Abstract

A Steiner triple system of order v is called (f, k)-rotational if it admits an automorphism consisting of f fixed points and k cycles of length (vf)/k. In this paper we deal with the existence of such Steiner triple systems when k = 2, f > 1 and show that an (f, 2)-rotational Steiner triple system of order v with f > 1 exists if and only if (i) v ≡ 1,3 (mod 6), (ii) f = 1,3 (mod 6), (iii) if vf ≡ 2 (mod 4) then v ≥ 3f; if vf = 0 (mod 4) then v = f or v ≥ 3f — 2, with the exceptions of v = 3f — 2 when f ≡ 1 (mod 12), v = 21 when f = 3, v = 3f — 2 or v = 3f + 10 when f ≡ 15 (mod 24), v = 3f + 4 when f = 3 (mod 12), v = 25 when f = 7, v = 3f – 2 when f ≡ 7 (mod 12), v = 27 when f = 9, v = 3f – 2 when f ≡ 21 (mod 24), v = 3f + 10 when f ≡ 9 (mod 24) and v = 3f + 4 when f = 9 (mod 12).

Keywords

Discrete Math Triple System Existence Condition Projection Property Steiner Triple System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Zhike Jiang
    • 1
  1. 1.Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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