Title
Antipode formulas for some combinatorial Hopf algebras
Department/School
Mathematics
Date
11-25-2016
Document Type
Article
Keywords
Combinatorial Hopf algebra, K-theory, Symmetric functions
Abstract
Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, Lam and Pylyavskyy studied six combinatorial Hopf algebras that can be thought of as K-theoretic analogues of the Hopf algebras of symmetric functions, quasisymmetric functions, noncommutative symmetric functions, and of the Malvenuto-Reutenauer Hopf algebra of permutations. They described the bialgebra structure in all cases that were not yet known but left open the question of finding explicit formulas for the antipode maps. We give combinatorial formulas for the antipode map for the K-theoretic analogues of the symmetric functions, quasisymmetric functions, and noncommutative symmetric functions.
Published in
Electronic Journal of Combinatorics
Citation/Other Information
Patrias, R. (2016). Antipode formulas for some combinatorial Hopf algebras. Electronic Journal of Combinatorics 23(4): P4.30. https://doi.org/10.37236/5949.