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In [4], a bijection between collections of reduced factorizations of elements of the symmetric group was described. Initially, this bijection was used to show the Schur positivity of the Stanley symmetric functions. Further investigations have revealed that our bijection has strong connections to other more familiar combinatorial algorithms. In this paper… (More)

In 1982, Richard Stanley introduced the formal series F X in order to enumerate reduced decompositions of a given permutation. I n 5 , he not only showed F X t o be symmetric, but in certain cases, F X w a s a S c h ur function. Stanley conjectured that for arbitrary , F X w as always Schur positive. Edelman and Greene subsequently proved this fact 11,,2.… (More)

In 1840, V. A. Lebesgue proved the following two series–product identities: n≥0

Beginning in 1893, L. J. Rogers produced a collection of papers in which he considered series expansions of infinite products. Over the years, his identities have been given a variety of partition theoretic interpretations and proofs. These existing combinatorial techniques, however, do not highlight the similarities and the subtle differences seen in so… (More)

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