Identical twin Steiner triple systems

Two Steiner triple systems, each containing precisely one Pasch configuration which, when traded, switches one system to the other, are called twin Steiner triple systems. If the two systems are isomorphic the systems are called identical twins. Hitherto, identical twins were only known for orders 21, 27 and 33. In this paper we construct infinite families of identical twin Steiner triple systems

Steiner triple systems with transrotational automorphisms

AbstractA Steiner triple system of order v is said to be k-transrotational if it admits an automorphism consisting of a fixed point, a transposition, and k cycles of length (v−3)k. Necessary and sufficient conditions are given for the existence of 1- and 2-transrotational Steiner triple systems

A note on reverse Steiner triple systems

A Steiner triple system of order v is called reverse if its automorphism group contains an involution having exactly one fixed point. Various constructions of such systems are given, in an attempt to prove that the necessary conditions of existence v ≡ 1, 3, 9 or 19 (mod 24) are also sufficient. © 1972.SCOPUS: ar.jinfo:eu-repo/semantics/publishe