On the number of edges in a uniform hypergraph with a range of permitted intersections

详细

The paper studies the quantity p(n, k, t₁, t₂) equal to the maximum number of edges in a k-uniform hypergraph with the property that the size of the intersection of any two edges lies in the interval [t₁, t₂]. Previously known upper and lower bounds are given. New bounds for p(n, k, t₁, t₂) are obtained, and the relationship between these bounds and known estimates is studied. For some parameter values, the exact values of p(n, k, t₁, t₂) are explicitly calculated.