Centre for Interdisciplinary Research in Computational Algebra (CIRCA) seminar

Rosemary Bailey will present Semi-Latin squares and their extensions.

Abstract: A Latin square of order n is an n × n square array, with one cell at the intersection of each row and each column, with one letter applied to each cell in such a way that each letter occurs once in each row and once in each column.

One way to generalize this is to replace the single cell in each row–column intersection by k cells, where k > 1. Then we use nk letters, each occurring once in each row and once in each column. These are called semi-Latin squares. Now the cells form the blocks of an incomplete-block design. We seek an allocation which produces a block desigh which is optimal by some statistical measure.

In some practical situations, it is reasonable to consider each column to consist of k sub-columns (called lines) each intersecting every cell in that column. Now we have to allow for both cells and lines in the statistical analysis. Finding good designs for this situation may need computer search.

Chris Jefferson will present Quickly finding canonical images of a graph in any group on the vertices.

Abstract: Tools like Nauty can find canonical images of huge graphs, and have been used by many people to solve problems in many areas of maths and computing.
However, there are things we might want to do beyond Nauty, such as finding canonical images within other groups, or finding canonical images of other combinatorial objects. It turns out that we can extend Nauty to solve many of these problems without having to make deep fundamental changes. I will show the types of problems we might want to solve, and when and how we can adapt Nauty to solve them.

Further details about this event, along with information about CIRCA, can be found on the CIRCA website https://circa.st-andrews.ac.uk