Constructing Regular Self-complementary Uniform Hypergraphs
Gosselin, Shonda. "Constructing Regular Self-complementary Uniform Hypergraphs." Journal of Combinatorial Designs 9(6) (November 2011): 439-454. DOI: 10.1002/jcd.20286. Early View (Online Version of Record published before inclusion in an issue)
In this paper, we examine the possible orders of t-subset-regular self-complementary k-uniform hypergraphs, which form examples of large sets of two isomorphic t-designs. We reformulate Khosrovshahi and Tayfeh-Rezaie's necessary conditions on the order of these structures in terms of the binary representation of the rank k, and these conditions simplify to a more transparent relation between the order n and rank k in the case where k is a sum of consecutive powers of 2. Moreover, we present new constructions for 1-subset-regular self-complementary uniform hypergraphs, and prove that these necessary conditions are sufficient for all k, in the case where t = 1.