Stability of extremal hypergraphs with applications to an edge-coloring problem

We obtain sharper stability results for hypergraphs that avoid a copy of an expanded complete 2-graph and for hypergraphs that avoid a Fan subhypergraph. We apply this to an edge-coloring problem on uniform hypergraphs, where we wish to find an n-vertex hypergraph with the largest number of colorings avoiding a rainbow copy of a fixed hypergraph F.