Cuspidal ribbon tableaux in affine type A

For any convex preorder on the set of positive roots affine type A, we classify and construct all associated cuspidal semicuspidal skew shapes. These combinatorial objects correspond to Specht modules for Khovanov-Lauda-Rouquier algebra A. Cuspidal shapes are ribbons, show that every shape has a unique ordered tiling by ribbons. This data provides an upper bound, in bilexicographic order Kostant partitions, labels simple factors modules.