An introduction to quasisymmetric Schur functions : Hopf algebras, quasisymmetric functions, and young composition tableaux / Kurt Luoto, Stefan Mykytiuk, Stephanie van Willigenburg
Introduction -- Classical combinatorial concepts -- Hopf algebras -- Composition tableaux and further combinatorial concepts -- Quasisymmetric Schur functions
Summary
An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is to provide a reference text for the basic theory of Hopf algebras, in particular the Hopf algebras of symmetric, quasisymmetric and noncommutative symmetric functions and connections between them. The second goal is to give a survey of results with respect to an exciting new basis of the Hopf algebra of quasisymmetric functions, whose combinatorics is analogous to that of the renowned Schur functions
