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Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results

Diane M. Donovan; Mike Grannell; Emine Ş. Yazıcı — 2020

Commentationes Mathematicae Universitatis Carolinae

We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of $t$ mutually orthogonal Latin squares of order $n$ to construct a set of $2 t$ mutually orthogonal Latin squares of order $n^{t}$ .

On independent sets

Anthony D. Forbes; Mike J. Grannell; Terry S. Griggs — 2005

Mathematica Slovaca

The design of the century

Anthony D. Forbes; Mike J. Grannell; Terry S. Griggs — 2007

Mathematica Slovaca

Biembeddings of symmetric configurations and 3-homogeneous Latin trades

Mike J. Grannell; Terry S. Griggs; Martin Knor — 2008

Commentationes Mathematicae Universitatis Carolinae

Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3-homogeneous Latin trades.

Properties of the Steiner triple systems of order 19.

Colbourn, Charles J.; Forbes, Anthony D.; Grannell, Mike J.; Griggs, Terry S.; Kaski, Petteri; Östergård, Patric R.J.; Pike, David A.; Pottonen, Olli — 2010

The Electronic Journal of Combinatorics [electronic only]

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