zbMATH — the first resource for mathematics

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
Keywords:
mitre configuration
Full Text:
References:
 [1] Colbourn, Graphs and Combin 10 pp 215– (1994) [2] Erdos, Creation in Mathematics 9 pp 25– (1976) [3] Fujiwara, J Combin Designs (2004) [4] On Steiner triple systems related to an Erdos conjecture, Master’s Thesis, School of Fundamental Science and Technology, Keio University, 2004. [5] Grannell, J Combin Design 8 pp 300– (2000) [6] Grannell, Ars Combinatoria 25A pp 55– (1988) [7] Lu, J Combin Theory, Series A 37 pp 136– (1984) [8] Ling, J Combin Designs 5 pp 443– (1997) [9] Wilson, Math Z 135 pp 303– (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.