Ottawa–Carleton
Discrete Mathematics Group

17 April 2009, 11.30am
HP4351, Carleton

We survey the current research into self-complementary uniform hypergraphs, and present several new results. In particular, we examine their possible orders, and the orders of these structures when they have the additional properties of regularity or transitivity.

The regular self-complementary uniform hypergraphs form examples of large sets of two isomorphic designs. In some of the literature, this is also known as halving the complete design into two isomorphic designs. We will present some new constructions for these objects, and obtain necessary and sufficient conditions on their order.