East elevation, overlooking driveway, private housing, Cotton Tree Housing Estate, Maroochydore

This pilot project at Cotton Tree, Maroochydore, on two adjacent, linear parcels of land has one of the properties privately owned while the other is owned by the public housing authority. Both owners commissioned Lindsay and Kerry Clare to design housing for their separate needs which enabled the two projects to be governed by a single planning and design strategy. This entailed the realignment of the dividing boundary to form two approximately square blocks which made possible the retention of an important stand of mature paperbark trees and gave each block a more useful street frontage. The scheme provides seven two-bedroom units and one single-bedroom unit as the private component, with six single-bedroom units, three two-bedroom units and two three-bedroom units forming the public housing. The dwellings are deployed as an interlaced mat of freestanding blocks, car courts, courtyard gardens, patios and decks. The key distinction between the public and private parts of the scheme is the pooling of the car parking spaces in the public housing to create a shared courtyard. The housing climbs to three storeys on its southern edge and falls to a single storey on the north-western corner. This enables all units and the principal private outdoor spaces to have a northern orientation. The interiors of both the public and private units are skilfully arranged to take full advantage of views, light and breeze.

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Internal cladding to north-east facade, Mooloomba House, Point Lookout, North Stradbroke Island

View of internal cladding to north-east facade as seen from dining studio.

Part of south-east elevation, Sunshine Coast University Library, Maroochydore

View to part of south-east elevation with skillion roof, corrugated steel sheeting and concrete block.

Steel cladding to south-east corner, Sunshine Coast University Library, Maroochydore

View to south-east corner, clad in corrugated steel sheeting with colonnade below.

Batten screen to north-east elevation, Sunshine Coast University Library, Maroochydore

View of timber batten screen to north-east elevation with verandah behind.

North-east verandah connection, Sunshine Coast University Library, Maroochydore

View of underside of verandah corrugated steel roofing, polycarbonate sheeting and north-east glass and floor connection.

North-east corner elevation, Sunshine Coast University Library, Maroochydore

View to north-east corner elevation, with entrance stair and timber batten screen to verandah.

South-east elevation, Sunshine Coast University Library, Maroochydore

View to south-east elevation; entrance stair, plywood and sheet steel cladding and colonnade, as seen from exterior.

Timber batten screen to north-east elevation, Sunshine Coast University Library, Maroochydore

View of timber batten screen to verandah behind and entrance stair, as seen from exterior.

Batten screen to north-east elevation, Sunshine Coast University Library, Maroochydore

View of timber batten screen to north-east elevation with verandah behind.

South-east elevation, Sunshine Coast University Library, Maroochydore

View to south-east elevation as seen from exterior.

Constructing and Deconstructing Latin Trades

This paper discusses existence results for latin trades and provides a Glueing Construction which is subsequently used to construct all latin trades of finite order greater than three.