Luoto, Kurt, Mykytiuk, Stefan, van Willigenburg, Stephanie
2013, XIV, 89 p. 75 illus.
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Comprehensive introduction to quasisymmetric functions for non-specialists
First summary of results in the blossoming field of quasisymmetric
Schur functions using Young composition tableaux, which generalize Young tableaux
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.