# Self-complementing permutations of k-uniform hypergraphs

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1 Faculty of Applied Mathematics Krakow

Abstract : A k-uniform hypergraph H = V; E is said to be self-complementary whenever it is isomorphic with its complement H over bar = V; Vk - E. Every permutation sigma of the set V such that sigmae is an edge of H over bar if and only if e is an element of E is called self-complementing. 2-self-comlementary hypergraphs are exactly self complementary graphs introduced independently by Ringel 1963 and Sachs 1962. For any positive integer n we denote by lambdan the unique integer such that n = 2lambdan c, where c is odd. In the paper we prove that a permutation sigma of 1, n with orbits O-1,

., O-m O m is a self-complementing permutation of a k-uniform hypergraph of order n if and only if there is an integer l >= 0 such that k = a2l + s, a is odd, 0

Author: ** Artur Szymański - Adam Pawel Wojda - **

Source: https://hal.archives-ouvertes.fr/