Ahmed M. Assaf, Alan Hartman, et al.
Discrete Mathematics
Let π be a permutation of the set {1, 2,..., υ} having f< υ fixed points and (υ — f)/2 disjoint transpositions. We investigate the existence of Steiner triple systems admitting π as an auto-morphism. When f = 1 such a system is known as a reverse Steiner triple system and it is known that reverse Steiner triple systems exist if and only if υ ≡ 1, 3, 9 or 19 (mod 24). In this paper we show that a Steiner triple system admitting π as an automorphism, and f > 1 exists if and only if υ ≡ 1 or 3(mod 6), f ≡ 1 or 3(mod 6), and either (υ — f ≡ 0(mod 4), and υ ⩾ 2f + 1) or (υ — f ≡ 2 (mod 4), and υ ⩾ 3f). © 1987, Academic Press Limited. All rights reserved.
Ahmed M. Assaf, Alan Hartman, et al.
Discrete Mathematics
Alan Hartman, Kenneth Nagin
UML Satellite Activities 2004
Alan Hartman
Discrete Mathematics
Alan Hartman, Andrei Kirshin, et al.
SEAPP 2002