Details of talk
|Title||Embedding partial Latin squares in Cayley tables|
|Presenter||Ian Wanless (Monash University)|
|Author(s)||Prof Ian Wanless|
A partial Latin square (PLS) can be thought of as a finite set of triples where no two distinct triples agree in more than one position. A group operation $\circ$ can be defined by triples of the form $(g,h,g\circ h)$. We say that a PLS embeds in a group if the set of triples which define the group contains an (appropriately relabelled) copy of the PLS. In this talk I will briefly survey some combinatorial problems related to embeddings of PLS in groups. I will then present some new results that answer questions published by Denes and Keedwell, and by Hirsch and Jackson. The most interesting of these questions turns out to be ``What is the smallest PLS that can be embedded into some infinite group but does not have an embedding into any finite group?''