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The resolution of the anti-mitre Steiner triple system conjecture. (English) Zbl 1089.05013
It is proved in this paper that an anti-mitre STS\((v)\) exists whenever \(v \equiv 1,3 \pmod{6}\) and \(v \neq 9\). The proof uses a tripling construction in cases when \(v \equiv 3 \pmod{6}\), and results of Y. Fujiwara [J. Comb. Des. 14, 237–250 (2006; Zbl 1089.05012 above)] and the reviewer and others [Graphs Comb. 10, 215–224 (1994; Zbl 0815.05017)] when \(v \equiv 1 \pmod{6}\).

MSC:
05B07 Triple systems
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