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

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