A virtual day trip to Ukraine

On Thursday, Rosemary and I took time out from the daily schedule to attend some virtual talks at the 25th meeting on “Combinatorial Configurations and their Applications” in Zaporizhzhia, Ukraine. Our CIRCA colleague Olexandr Konovalov was one of the organisers, amd also spoke, as did Özgür Azgün, also from Computer Science at St Andrews.

Of course, most of the talks were in Ukrainian, a language of which I have no knowledge; but Olexandr and Özgür spoke in English: their titles were “Open science and reproducible research” and “Jupyter notebooks for interactive constraint programming”.

Olexandr’s subject is of course a hot topic in science at present; some speak of a crisis in reproducibility and blame it on unintelligent use of various statistical tools. But his talk was more about the use of computers in mathematics, a topic I have recently mentioned here. Jupyter notebooks (something I have heard of but not used myself) have the facility of combining code, computational results and textual comments in a single editable document, so that others can understand and check the code, run it themselves, or run the code with changes (for example, to the parameters). Özgür’s talk followed on nicely; he gave us several examples of using a Jupyter notebook for constraint programming languages (a St Andrews speciality) to solve actual problems.

This brought to my mind something I have discussed and asked many people about: finding all Sylvester designs. (These are block designs with 36 points and 48 blocks of size 6, two points lying in two blocks if they are adjacent in the distance-transitive Sylvester graph, and in a unique block otherwise. Such designs are equally good under the standard A, D and E optimality criteria used by statisticians. We know three such designs, distinguished by the orders of their automorphism groups (these are 1440 (the full group of the graph), 144 and 1. I would very much like a complete classification!