Catalogue of manuscripts from the Hayes Collection in the University of Queensland Library

Index to correspondence and manuscript material on literary and historical matters, mostly in Queensland and New South Wales, Australia held in the Fryer Library, University of Queensland - UQFL2. Authors and subjects include J.H.M. Abbott, Archer Family, E. Armitage, R. Bedford, H.S. Bloxome, E.J. Brady, 'Broadside', F. Broomfield, A.H. Chisholm, C.B. Christesen, R.H. Croll, Z. Cross, F.W.S. Cumbrae-Stewart, E. Dark, D. Deamer, C.J. Dennis, J. Devaney, E.M. England, P. Fitzgerald, R.D. Fitzgerald, Dame Mary Gilmore, C. Gittins, A.L. Gordon (criticism), P. Grano, M. Haley, W.A. Horn, R.G. Howarth, J. Howlett Ross, E.H. Lane, H. Lane, F.J. McAuley, D. McConnel, G. McCrae, K. (S) Mackenzie, P. Miles, J.K. Moir, C.P. Mountford, A. Muir, D.A. O'Brien, J.H. O'Dwyer, W.H. Ogilvie, M. Potter, T. Playford, H. Power, Queensland Authors' and Artists' Association, I. Southall, W. Sowden, A.G. Stephens, P.R. Stephensen, H. Tyron, A.J. Vogan, B. Vrepont, T. Welsby, H.R. White and Duke of Windsor. Also personal papers of Father Hayes, relating to his activities as parish priest.

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.

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.

Critical sets for families of Latin squares

In this paper I give details of new constructions for critical sets in latin squares. These latin squares, of order n, are such that they can be partitioned into four subsquares each of which is based on the addition table of the integers module n/2, an isotopism of this or a conjugate.

Critical sets in direct products of back circulant Latin squares

To date very Few families of critical sets for latin squares are known. The only previously known method for constructing critical sets involves taking a critical set which is known to satisfy certain strong initial conditions and using a doubling construction. This construction can be applied to the known critical sets in back circulant latin squares of even order. However, the doubling construction cannot be applied to critical sets in back circulant latin squares of odd order. In this paper a family of critical sets is identified for latin squares which are the product of the latin square of order 2 with a back circulant latin square of odd order. The proof that each element of the critical set is an essential part of the reconstruction process relies on the proof of the existence of a large number of latin interchanges.

On the distance between distinct group Latin squares

In an article in 1992, Drapal addressed the question of how far apart the multiplication tables of two groups can be? In this article we continue this investigation; in particular, we study the interaction between partial equalities in the multiplication tables of the two groups and their subgroup structure. (C) 1997 John Wiley & Sons, Inc.

Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

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.

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.