The Cyclically Resolvable Steiner Triple Systems of Order 57

Abstract

A resolution of a Steiner triple system of order v (STS(v)) is point-cyclic if it has an automorphism permuting the points in one cycle. An STS(v) is cyclically resolvable if it has at least one point-cyclic resolution. Cyclically resolvable STS(v)s have important applications in Coding Theory. They have been classified up to v=45 and before the present work v=57 was the first open case. There are 2,353,310 cyclic STS(57)s. We establish that 155,966 of them are cyclically resolvable yielding 3,638,984 point-cyclic resolutions which we classify with respect to their automorphism groups and to the availability of some configurations.

Keywords

• Steiner triple system
• cyclically resolvable
• automorphism
• point-cyclic resolution
• anti-Pasch
• anti-mitre