Geodesic
A note on k-uniform self-complementary hypergraphs of given order
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 1, pp. 199-202

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We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if nk is even.
Keywords: self-complementing permutation, self-complementary hypergraph, k-uniform hypergraph, binomial coefficients 
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Szymański, Artur; Wojda, A. A note on k-uniform self-complementary hypergraphs of given order. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 1, pp. 199-202. http://geodesic.mathdoc.fr/item/DMGT_2009_29_1_a11/