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Symmetric Functions and Generating Functions for Descents and Major Indices in Compositions
Evan Fuller1 and Jeffrey Remmel2
1Department of Mathematics, Montclair State University, Montclair, New Jersey 07043, USA
fullere@montclair.edu
2Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA
remmel@math.ucsd.edu
Annals of Combinatorics 14 (1) pp.103-121 Springer, 2010
AMS Subject Classification: 05A15, 05E05
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.
Keywords: permutation statistics, compositions, symmetric functions

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