EXTENDING POTOČNIK AND ŠAJNA'S CONDITIONS ON VERTEX-TRANSITIVE SELF-COMPEMENTARY k-HYPERGRAPHS

Linda Lesniak (1) , Henri Thuillier (2) , Adam Pawel Wojda (3)

1 Western Michigan University [Kalamazoo]
2 UO - Université d'Orléans
3 AGH UST - AGH University of Science and Technology [Krakow, PL]

Abstract : Let l be a positive integer, k = 2l or k = 2l + 1 and let n be a positive integer with $n \equiv 1$ (mod $2^{l+1}$). Potocnik and Sajna showed that if there exists a vertex-transitive self-complementary k-hypergraph of order n, then for every prime p we have $p^{n_{(p)}} \equiv 1 \pmod {2^{l+1}}$ (where $n_{(p)}$ denotes the largest integer $i$ for which $p^i$ divides $n$). Here we extend their result to any integer k and a larger class of integers n.

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Linda Lesniak, Henri Thuillier, Adam Pawel Wojda. EXTENDING POTOČNIK AND ŠAJNA'S CONDITIONS ON VERTEX-TRANSITIVE SELF-COMPEMENTARY k-HYPERGRAPHS. 2019. ⟨hal-02302371⟩