Journal article
Double posets and the antipode of QSym
The Electronic journal of combinatorics, v 24(2), 2
05 May 2017
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
A quasisymmetric function is assigned to every double poset (that is, every finite set endowed with two partial orders) and any weight function on its ground set. This generalizes well-known objects such as monomial and fundamental quasisymmetric functions, (skew) Schur functions, dual immaculate functions, and quasisymmetric (P, omega)-partition enumerators. We prove a formula for the antipode of this function that holds under certain conditions (which are satisfied when the second order of the double poset is total, but also in some other cases); this restates (in a way that to us seems more natural) a result by Malvenuto and Reutenauer, but our proof is new and self-contained. We generalize it further to an even more comprehensive setting, where a group acts on the double poset by automorphisms.
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Details
- Title
- Double posets and the antipode of QSym
- Creators
- Darij Grinberg - University of Minnesota System
- Publication Details
- The Electronic journal of combinatorics, v 24(2), 2
- Publisher
- Electronic Journal Of Combinatorics
- Number of pages
- 47
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000408644700008
- Scopus ID
- 2-s2.0-85019053568
- Other Identifier
- 991021862242904721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied