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Abstract:
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In this paper, we examine the possible orders of t-subset-regular selfcomplementary
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 su cient for all k,
in the case where t = 1. |