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Recent Trends in Quasisymmetric Functions

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Recent Trends in Algebraic Combinatorics

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 16))

Abstract

This article serves as an introduction to several recent developments in the study of quasisymmetric functions. The focus of this survey is on connections between quasisymmetric functions and the combinatorial Hopf algebra of noncommutative symmetric functions, appearances of quasisymmetric functions within the theory of Macdonald polynomials, and analogues of symmetric functions. Topics include the significance of quasisymmetric functions in representation theory (such as representations of the 0-Hecke algebra), recently discovered bases (including analogues of well-studied symmetric function bases), and applications to open problems in symmetric function theory.

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Acknowledgements

I am very grateful to Hélène Barcelo, Gizem Karaali, and Rosa Orellana for inviting me to produce this chapter. I would also like to thank Ed Allen, Susanna Fishel, Josh Hallam, Jim Haglund, and John Shareshian for helpful feedback along the way. Finally, I greatly appreciate the insightful comments from a diligent anonymous referee.

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  1. Department of Mathematics, Wake Forest University, Winston-Salem, NC, USA

    Sarah K. Mason

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  1. Mathematical Sciences Research Institute , Berkeley, CA, USA

    Hélène Barcelo

  2. Department of Mathematics, Pomona College, Claremont, CA, USA

    Gizem Karaali

  3. Department of Mathematics, Dartmouth College, Hanover, NH, USA

    Rosa Orellana

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Mason, S.K. (2019). Recent Trends in Quasisymmetric Functions. In: Barcelo, H., Karaali, G., Orellana, R. (eds) Recent Trends in Algebraic Combinatorics. Association for Women in Mathematics Series, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-030-05141-9_7

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