Invited Talks

In 2009, Peter Cameron introduced a common generalization of various classes of combinatorial designs such as balanced incomplete block designs, resolvable designs and orthogonal arrays. Generalized covering and packing designs can be defined in analogous way. These objects bring into this framework further classes of designs, including covering and packing arrays, Howell designs, monogamous cycle decompositions and Kirkman signal sets. In this talk, I will review known results on generalized designs, packings and coverings, and discuss interesting open questions which arise in the search for further examples of optimal generalized packing designs. This talk will include discussions of joint work with Robert Bailey, Michael Cavers, Peter Danziger and Karen Meagher.