An Introduction to Quasisymmetric Schur Functions: Hopf Algebras, Quasisymmetric Functions, and Young Composition Tableaux (SpringerBriefs in Mathematics)

__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. ¿¿¿ ¿An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. This book introduces readers to the algebra of quasisymmetric functions and its fundamental theory. Results and relevant new contributions are included which pertains to the dynamic new basis of quasisymmetric Schur functions. A state-of-the-art summary is included with respect to an exciting new basis of algebra, which is the basis of quasisymmetric Schur functions, whose combinatorics is analogous to that of the renowned Schur functions.¿ Front Matter....Pages i-xiv Introduction....Pages 1-3 Classical combinatorial concepts....Pages 5-17 Hopf algebras....Pages 19-50 Composition tableaux and further combinatorial concepts....Pages 51-62 Quasisymmetric Schur functions....Pages 63-81 Back Matter....Pages 83-89