Flora Bowditch

Resolvable Designs and their Applications

Resolvable designs are a particularly interesting class of balanced incomplete block designs. They hold the extra property that their block set can be partitioned into parallel classes. Resolvable designs make appearances in various fields of mathematics. They are related to finite affine planes and graph decompositions, but can also be used for scheduling problems and the design of statistical experiments. In this talk, we will give the definition of a resolvable design, look at some examples and non-examples, and examine the necessary conditions for their existence. We will then discuss the theorem from Ray-Chaudhuri and Wilson which gives the asymptotic existence of resolvable designs. To conclude, we will look at some applications of these designs, including the solution to the famous “Kirkman's Schoolgirls Problem”.