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Infinite classes of anti-mitre and 5-sparse Steiner triple systems. (English) Zbl 1089.05012
Constructions for Steiner triple systems admitting no mitre configuration are given, demonstrating that anti-mitre Steiner triple systems exist for 13/14 of the admissible orders. It has since been shown that an anti-mitre STS\((v)\) exists whenever \(v \equiv 1,3 \pmod{6}\) and \(v \neq 9\), see A. Wolfe, [J. Comb. Des. 14, 229–236 (2006; Zbl 1089.05013 below)]. In addition, the paper presents a new construction for 5-sparse (that is, both anti-Pasch and anti-mitre) Steiner triple systems.

MSC:
05B07 Triple systems
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