20 research outputs found
Tournaments, 4-uniform hypergraphs, and an exact extremal result
We consider -uniform hypergraphs with the maximum number of hyperedges
subject to the condition that every set of vertices spans either or
exactly hyperedges and give a construction, using quadratic residues, for
an infinite family of such hypergraphs with the maximum number of hyperedges.
Baber has previously given an asymptotically best-possible result using random
tournaments. We give a connection between Baber's result and our construction
via Paley tournaments and investigate a `switching' operation on tournaments
that preserves hypergraphs arising from this construction.Comment: 23 pages, 6 figure
The extended binary quadratic residue code of length 42 holds a 3-design
The codewords of weight of the extended binary quadratic
residue code are shown to hold a design of parameters Its
automorphism group is isomorphic to . Its existence can be explained
neither by a transitivity argument, nor by the Assmus-Mattson theorem.Comment: 6 pages. Second versio
The solvable subgroups of large order of L2(p) , p≥5
By using the following theoretical and computational algorithms , we determined the solvable subgroups of large order of the finite non-abelian simple linear groups G = L2(p) = PSL(2,p) , for p≥5 and p is a prime number , also their presentations and permutation representations have been found
An Infinite Family of Connected 1-Factorisations of Complete 3-Uniform Hypergraphs
A connected 1-factorisation is a 1-factorisation of a hypergraph for which
the union of each pair of distinct 1-factors is a connected hypergraph. A
uniform 1-factorisation is a 1-factorisation of a hypergraph for which the
union of each pair of distinct 1-factors is isomorphic to the same
subhypergraph, and a uniform-connected 1-factorisation is a uniform
1-factorisation in which that subhypergraph is connected. Chen and Lu [Journal
of Algebraic Combinatorics, 46(2) 475--497, 2017] describe a family of
1-factorisations of the complete 3-uniform hypergraph on vertices, where
is a prime power. In this paper, we show that their
construction yields a connected 1-factorisation only when or
for some odd prime , and a uniform 1-factorisation only for (each
of these is a uniform-connected 1-factorisation).Comment: 11 page