We give a combinatorial proof of the skew Kostka analogue of the K-saturation theorem. More precisely, for any positive integer k, we give an explicit injection from the set of skew semistandard Young tableaux with skew shape k\lambda/k\mu{ } and type k\nu{ } to the set of skew semistandard Young tableaux of shape \lambda/\mu{ } and type \nu. Based on this method, we pose some natural conjectural refinements on related problems.
Categories: math.CO