Combinatorial Hopf algebras and K-homology of Grassmanians
By Thomas Lam, Pavlo Pylyavskyy. 2007
124 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9ea683beca2f6d485caf638c1d789f1fd78671eb
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
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Citations in the corpus
- Combinatorial Hopf algebras (2008, background): “Among other examples we find: the Faà di Bruno algebra, variations of the symmetric functions: Sym, NSym, FSym, QSym, FQSym, PQSym, (Aguiar-Sottile [2, 3], Bergeron-Hohlweg [4], Chapoton-Livernet [12], Livernet [33], Malvenuto-Reutenauer [44], Hivert-Novelli-Thibon [25], Palacios-Ronco [48]), exampl”