## 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

### Keywords:

mitre configuration; Pasch configuration; 5-sparse STS

Zbl 1089.05013
Full Text:

### References:

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