Geodesic
Antipode formulas for some combinatorial Hopf algebras
Rebecca Patrias1
1Université du Québec à Montréal
The electronic journal of combinatorics, Tome 23 (2016) no. 4
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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.
DOI : 10.37236/5949
Classification : 05E05, 14M15
Mots-clés : combinatorial Hopf algebra, \(K\)-theory, symmetric functions

Rebecca Patrias  1

1 Université du Québec à Montréal 
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     title = {Antipode formulas for some combinatorial {Hopf} algebras},
     journal = {The electronic journal of combinatorics},
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     number = {4},
     doi = {10.37236/5949},
     zbl = {1351.05234},
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Rebecca Patrias. Antipode formulas for some combinatorial Hopf algebras. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/5949

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