Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

A minimal defining set of a Steiner triple system on a points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v + 1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on, 3" points; we construct minimal defining sets of volumes varying by as much as 7(n-/-).

Girls and tea ladies: involvement of Australian female athletes and administrators in the 1956 Melbourne Olympic Games

This article focuses on the 1956 Olympic Games in order to consider and ascertain the role and place of women in Australian society, generally, and, more specifically, in Australian 'sport' as both athletes and sporting administrators.

A discussion on the Heteracanthocephalidae Petrochenko, 1956 (Acanthocephala : Palaeacanthocephala)

Several heteracanthocephalid specimens were recovered from the flatfish Rhombosolea leporina (Gunther), a host of Heteracanthocephalus peltorhamphi (Baylis, 1944) Petrochenko, 1956 from New Zealand. Unlike H. peltorhamphi, these new specimens have trunk spines. Measurements and proboscis armament of the new specimens are consistent with the worms being Aspersentis minor Edmonds & Smales, 1992 originally described from the Australian flounder Rhombosolea tapirina Gunther. A review of the family Heteracanthocephalidae Petrochenko, 1956 was undertaken to assess the validity of its four genera and eight species. The validity of Aspersentis megarhynchus (Linstow, 1892) Golvan, 1960 (syn. Echinorhynchus megarhynchus Linstow, 1892) is questioned. E. megarhynchus is not considered to be an heteracanthocephalid and is relegated to a species inquirenda. A. megarhynchus (Linstow, 1892) of Golvan (1960) nec E. megarhynchus Linstow, 1892 is considered a synonym of A. austrinus Van Cleave, 1929. The monotypic genus Heteracanthocephalus Petrochenko, 1956 is proposed as a synonym of Aspersentis Van Cleave, 1929 because there appear to be insufficient morphological differences between them. Aspersentis peltorhamphi n. comb. is proposed for Heteracanthocephalus peltorhamphi. The monotypic genus Sachalinorhynchus Krotov & Petrochenko in Petrochenko, 1956 is considered valid, but the other heteracanthocephalid genus, Bullockrhynchus Chandra, Rao & Shyamasundari, 1985, also monotypic, is not. B. indicus Chandra, Rao & Shyamasundari, 1985 possesses more features resembling rhadinorhynchids than heteracanthocephalids but only females are known, and therefore the genus and species cannot be placed. There are currently four valid species of Aspersentis and one of Sachalinorhynchus.

Steiner trades that give rise to completely decomposable latin interchanges

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges.

A conjecture on small embeddings of partial Steiner triple systems

A well-known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.