The grid shading problem is the problem of proving the unimodality of the sequence {a_1, a_2, ..., a_(m n)}, where for fixed m and n, a_i is the number of partitions of i with at most m parts and largest part at most n. The grid shading problem was solved by Sylvester using invariant theory. Proctor gave the first elementary proof of this result. The q-binomial coefficients give the generating function for this sequence.
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