Geodesic
Extending Potočnik and Šajna's conditions on the existence of vertex-transitive self-complementary $k$-hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 1, pp. 225-231

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Let 𝓁 be a positive integer, k=2^𝓁 or k=2^𝓁+1, and let n be a positive integer with n ≡ 1 (mod 2^𝓁+1). For a prime p, n_(p) denotes the largest integer i such that p^i divides n. Potočnik and Šajna showed that if there exists a vertex-transitive self-complementary k-hypergraph of order n, then for every prime p we have p^n_(p)≡ 1 ( 2^𝓁+1 ). Here we extend their result to a larger class of integers k.
Keywords: vertex-transitive $k$-hypergraphs, self-complementary hypergraphs 
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Lesniak, Linda; Thuiller, Henri; Wojda, Adam Paweł. Extending Potočnik and Šajna's conditions on the existence of vertex-transitive self-complementary $k$-hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 1, pp. 225-231. http://geodesic.mathdoc.fr/item/DMGT_2023_43_1_a14/