### Abstract:

A cyclically t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation 2 Sym.V/ such that the sets E; E ; E 2; : : : ; E t1 partition the set of all k-subsets of V. Such a permutation is called a
.t; k/-complementing permutation. The cyclically t-complementary
k-hypergraphs are a natural and useful generalization of the self-complementary
graphs, which have been studied extensively in the
past due to their important connection to the graph isomorphism
problem.
For a prime p, we characterize the cycle type of the .pr ; k/-
complementing permutations 2 Sym.V/ which have order a
power of p. This yields a test for determining whether a permutation
in Sym.V/ is a .pr ; k/-complementing permutation, and an
algorithm for generating all of the cyclically pr-complementing k-
hypergraphs of order n, for feasible n, up to isomorphism. We also
obtain some necessary and sufficient conditions on the order of these structures. This generalizes previous results due to Ringel, Sachs, Adamus, Orchel, SzymaÂ«ski, Wojda, Zwonek, and Bernaldez.