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In this paper we provide a bijective proof of a theorem of Garsia and Gessel describing the generating function of the major index over the set of all permutations of [n] = {1, ..., n} which are shuffles of given disjoint ordered sequences π 1 , ..., π k whose union is [n]. The proof is based on a result (an " insertion lemma ") of Haglund, Loehr, and… (More)

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