Title
Double posets and the antipode of QSym
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.
Year
Venue
Keywords
2017
ELECTRONIC JOURNAL OF COMBINATORICS
antipodes,double posets,Hopf algebras,posets,P-partitions,quasisymmetric functions
Field
DocType
Volume
Discrete mathematics,Combinatorics,Weight function,Finite set,Automorphism,Omega,Skew,Monomial,Quasisymmetric function,Partially ordered set,Mathematics
Journal
24.0
Issue
ISSN
Citations 
2.0
1077-8926
1
PageRank 
References 
Authors
0.39
2
1
Name
Order
Citations
PageRank
darij grinberg1133.65