@Article{Szymański2005,
author = "Szymański, Artur",
title = "A note on self-complementary 4-uniform hypergraphs",
journal = "Opuscula Math.",
year = "2005",
volume = "25",
number = "2",
pages = "319--323",
doi = "http://dx.doi.org/10.7494/OpMath.2005.25.2.319",
url = "http://dx.doi.org/10.7494/OpMath.2005.25.2.319",
abstract = "We prove that a permutation \(\theta\) is complementing permutation for a \(4\)-uniform hypergraph if and only if one of the following cases is satisfied: (i) the length of every cycle of \(\theta\) is a multiple of \(8\), (ii) \(\theta\) has \(1\), \(2\) or \(3\) fixed points, and all other cycles have length a multiple of \(8\), (iii) \(\theta\) has \(1\) cycle of length \(2\), and all other cycles have length a multiple of \(8\), (iv) \(\theta\) has \(1\) fixed point, \(1\) cycle of length \(2\), and all other cycles have length a multiple of \(8\), (v) \(\theta\) has \(1\) cycle of length \(3\), and all other cycles have length a multiple of \(8\). Moreover, we present algorithms for generating every possible \(3\) and \(4\)-uniform self-complementary hypergraphs.",
keywords = "complementing permutation, self-complementary hypergraph, \(k\)-uniform hypergraph",
issn = "1232-9274"
}