Packing cliques in 3‐uniform hypergraphs

For positive integers n ≥ k ≥ t , a collection B of k ‐subsets of an n ‐set X is called a t ‐packing if every t ‐subset of X appears in at most one set in B . In this paper, we investigate the existence of the maximum 3‐packings whenever n is sufficiently larger than k . When n ≢ 2( mod k − 2 ) , the optimal value for the size of a 3‐packing is settled. In other cases, lower and upper bounds are obtained where mostly differ by an additive constant depending only on k but one case that they differ by a linear bound in n .