## Abstract

An *almost t-complementary k-hypergraph* is a *k*-uniform hypergraph with vertex set *V* and edge set *E* for which there exists a permutation \(\theta \in Sym(V)\) such that the sets \(E, E^\theta , E^{\theta ^2}, \ldots , E^{\theta ^{t-1}}\) partition the set of all *k*-subsets of *V* minus one edge. Such a permutation \(\theta \) is called an *almost (t, k)-complementing permutation*. Almost *t*-complementary *k*-hypergraphs are a natural generalization of almost self-complementary graphs, which were previously studied by Clapham, Kamble et al., and Wojda. We prove that there exists an almost *p*-complementary *k*-hypergraph of order *n* whenever the base-*p* representation of *k* is a subsequence of the base-*p* representation of *n*, where *p* is prime.

## Keywords

Almost self-complementary hypergraph Uniform hypergraph Almost (*t, k*)-complementing permutation

## Mathematics Subject Classification

05C65 05E20 05C25 05C85## Preview

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## Notes

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