Anti-Ramsey number of matchings in hypergraphs

A k-matching in a hypergraph is a set of k edges such that no two of these edges intersect. The anti-Ramsey number of a k-matching in a complete s-uniform hypergraph H on n vertices, denoted by ar(n,s,k), is the smallest integer c such that in any coloring of the edges of H with exactly c colors, there is a k-matching whose edges have distinct colors. The Turán number, denoted by ex(n,s,k), is the the maximum number of edges in an s-uniform hypergraph on n vertices with no k-matching. For k≥3, we conjecture that if n>sk, then ar(n,s,k)=ex(n,s,k−1)+2. Also, if n=sk, then ar(n,s,k)={ex(n,s,k−1)+2if  k