Generating Functions for Permutations which Contain a Given Descent Set
Keyword(s):
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.
2017 ◽
Vol 2019
(17)
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pp. 5389-5440
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2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
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2013 ◽
Vol 313
(23)
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pp. 2712-2729
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1950 ◽
Vol 2
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pp. 334-343
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1982 ◽
Vol 33
(1)
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pp. 76-85
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