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.

Original languageEnglish (US)
Article numberrnm125
JournalInternational Mathematics Research Notices
Volume2007
DOIs
StatePublished - 2007

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