A new derivation of the generating function for the major index

We present a new proof of the well-known combinatorial result [nk]q = [Sigma]w qMaj(w) where w is a permutation of 0k1n-k, by showing a bijection between the set of partitions of an integer m that fit in a k x n - k rectangle and the set consisting of all permutations w of 0k1n-k having Maj(w) = m.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28617/1/0000429.pd