On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

'Homescapes' and identity reformations in Australian multicultural drama

A consideration of identity formation in contemporary Australian multicultural theatre is offered through a re-assessment of the unsettled (and unsettling) constructions of Australia as 'home' in the work of three playwrights. William Yang's Sadness disrupts a localized perception of home, space, and cultural communities to amalgamate two disparate communities (the queer/homosexual community in Sydney and the Asian-Australian, or 'Austasian' community) into a reconfigured Australian identity. Janis Balodis's The Ghosts Trilogy uses many actors who play across the unsettled lines of history, amid numerous voices, homes, and homelands that indicate the enormity of what 'Australia' comes to signify. Noelle Janaczewska's The History of Water constructs a way of locating the self by means of a metaphoric home as each character establishes herself on a psychic plane rather than choosing the strictly physical locations to which she has access. In their interrogations of home and homeland, these plays challenge assumptions regarding identity, disrupt notions of the ultimate ownership of land/culture by anyone, and problematize the idea of settlement as it is currently articulated in Australia.

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.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Latin interchanges and direct products

In this paper we focus on the identification of latin interchanges in latin squares which are the direct product of latin squares of smaller orders. The results we obtain on latin interchanges will be used to identify critical sets in direct products. This work is an extension of research carried out by Stinson and van Rees in 1982.