Combinatorial Hopf algebras and K-homology of Grassmanians

Thomas Lam; Pavlo Pylyavskyy

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arXiv · 0705.2189

Combinatorial Hopf algebras and K-homology of Grassmanians

Thomas Lam·Pavlo Pylyavskyy

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Abstract

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical ``square'' of Hopf algebras consisting of symmetric functions, quasisymmetric functions, noncommutative symmetric functions and the Malvenuto-Reutenauer Hopf algebra of permutations. In addition, we develop a theory of set-valued P-partitions and study three new families of symmetric functions which are weight generating functions of reverse plane partitions, weak set-valued tableaux and valued-set tableaux.

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Thomas Lam, Pavlo Pylyavskyy. 2007-05-15. Combinatorial Hopf algebras and K-homology of Grassmanians. https://arxiv.org/abs/0705.2189

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