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An Introduction to Quasisymmetric Schur Functions

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Abstract

A brief history of the Hopf algebra of quasisymmetric functions is given, along with their appearance in discrete geometry, representation theory and algebra. A discussion on how quasisymmetric functions simplify other algebraic functions is undertaken, and their appearance in areas such as probability, topology, and graph theory is also covered. Research on the dual algebra of noncommutative symmetric functions is touched on, as is a variety of extensions to quasisymmetric functions. What is known about the basis of quasisymmetric Schur functions is also addressed.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada

    Kurt Luoto & Stephanie van Willigenburg

  2. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada

    Stefan Mykytiuk

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  1. Kurt Luoto
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  2. Stefan Mykytiuk
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© 2013 Kurt Luoto, Stefan Mykytiuk, Stephanie van Willigenburg

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Luoto, K., Mykytiuk, S., van Willigenburg, S. (2013). Introduction. In: An Introduction to Quasisymmetric Schur Functions. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7300-8_1

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