Self-complementary hypergraphs and their self-complementing permutations

A k–uniform hypergraph H = ( V ; E ) is called self-complementary if there is a permutation σ : V → V , called self-complementing, such that for every k–subset e of V, e ∈ E if and only if σ ( e ) ∉ E . In other words, H is isomorphic with H ′ = ( V ; ( V k ) − E ) . present paper, for every k, ( 1 ⩽ k ⩽ n ) , we give a characterization of self-complementig permutations of k–uniform self-complementary hypergraphs of the order n. This characterization implies the well known results for self-complementing permutations of graphs, given independently in the years 1962 – 1963 by Sachs and Ringel, and those obtained for 3–uniform hypergraphs by Kocay, for 4–uniform hypergraphs by Szymański, and for general (not uniform) hypergraphs by Zwonek.