Geodesic
Generating functions for permutations which contain a given descent set
The electronic journal of combinatorics, Tome 17 (2010)
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A large number of generating functions for permutation statistics can be obtained by applying homomorphisms to simple symmetric function identities. In particular, a large number of generating functions involving the number of descents of a permutation $\sigma$, $des(\sigma)$, arise in this way. For any given finite set $S$ of positive integers, we develop a method to produce similar generating functions for the set of permutations of the symmetric group $S_n$ whose descent set contains $S$. Our method will be to apply certain homomorphisms to symmetric function identities involving ribbon Schur functions.
DOI : 10.37236/299
Classification : 05A15, 68R15, 06A07
Mots-clés : ribbon Schur functions, descent sets, generating functions, permutation statistics 
@article{10_37236_299,
     author = {Jeffrey Remmel and Manda Riehl},
     title = {Generating functions for permutations which contain a given descent set},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/299},
     zbl = {1193.05016},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/299/}
}
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%A Jeffrey Remmel
%A Manda Riehl
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%J The electronic journal of combinatorics
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Jeffrey Remmel; Manda Riehl. Generating functions for permutations which contain a given descent set. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/299

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