2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128991Motivated 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.35 pages, 10 figuresCombinatoricsAlgebraic Geometry05E05; 57T05; 14M15text