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doi:10.1016/0012-365X(90)90154-A 
Copyright © 1990 Published by Elsevier Science B.V. All rights reserved.
Communication
A new derivation of the generating function for the major index
Received 7 November 1989.
Communicated by I. Gessel
Available online 28 March 2002.
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Abstract
We present a new proof of the well-known combinatorial result [nk]q = Σw 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 × n − k rectangle and the set consisting of all permutations w of 0k1n−k having Maj(w) = m.
