Abstract
In [18], Mendes and Remmel showed how Gessel’s generating function for the distributions of the number of descents, the major index, and the number of inversions of permutations in the symmetric group could be derived by applying a ring homomorphism defined on the ring of symmetric functions to a simple symmetric function identity. We show how similar methods may be used to prove analogues of that generating function for compositions.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Fuller, E., Remmel, J. Symmetric Functions and Generating Functions for Descents and Major Indices in Compositions. Ann. Comb. 14, 103–121 (2010). https://doi.org/10.1007/s00026-010-0054-5
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DOI: https://doi.org/10.1007/s00026-010-0054-5