Arcs and ovals in steiner triple systems
Several constructions of Steiner triple systems (STS) with ovals are given. For every v ≡ 3 or 7 mod 12 there are STS's with hyperovals, for every v ≡ 1 or 3 mod 6 there are STS's with ovals, and for infinitely many v ≡ 1 or 3 mod 6 there are STS's without ovals. The ovals may be classified by their complementary sets, the so-called counterovals. Several questions remain open.
KeywordsAutomorphism Group Incidence Matrix Steiner Triple System Balance Incomplete Block Design Steiner System
Unable to display preview. Download preview PDF.
- 5.M. Hall Combinatorial Theory. 2nd ed., Blaisdell, Waltham, Mass. 1975.Google Scholar
- 7.J.W.P. Hirschfeld Projective Geometries over Finite Fields. Oxford University Press 1979.Google Scholar
- 8.D.E. Knuth A permanent inequality. Amer. Math. Monthly 1981, 731–740.Google Scholar
- 9.C.C. Lindner A. Rosa (eds.) Topics on Steiner systems. Annals Discrete Math. 7 (1980), 317–349.Google Scholar
- 12.W. Piotrowski Oral communication.Google Scholar
- 13.S. Segre Lectures on modern geometry. Cremonese 1960.Google Scholar
- 16.H. Zeitler Ovals in STS(13). Math. Semesterber., to appearGoogle Scholar