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Dual immaculate creation operators and a...
Grinberg, Darij...

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Dual immaculate creation operators and a dendriform algebra structure on the quasisymmetric functions by Grinberg, Darij ( Author )
Lemonjar Open Access
N.A
01-10-2014
The dual immaculate functions are a basis of the ring QSym of quasisymmetric functions, and form one of the most natural analogues of the Schur functions. The dual immaculate function corresponding to a composition is a weighted generating function for immaculate tableaux in the same way as a Schur function is for semistandard Young tableaux; an "immaculate tableau" is defined similarly to a semistandard Young tableau, but the shape is a composition rather than a partition, and only the first column is required to strictly increase (whereas the other columns can be arbitrary; but each row has to weakly increase). Dual immaculate functions have been introduced by Berg, Bergeron, Saliola, Serrano and Zabrocki in arXiv:1208.5191, and have since been found to possess numerous nontrivial properties. In this note, we prove a conjecture of Mike Zabrocki which provides an alternative construction for the dual immaculate functions in terms of certain "vertex operators". The proof uses a dendriform structure on the ring QSym; we discuss the relation of this structure to known dendriform structures on the combinatorial Hopf algebras FQSym and WQSym.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1410.0079
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