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Asymmetric Function Theory

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Schubert Calculus and Its Applications in Combinatorics and Representation Theory (ICTSC 2017)

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Abstract

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.

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Acknowledgements

OP was partially supported by a Mathematical Sciences Postdoctoral Research Fellowship (#1703696) from the National Science Foundation. We are grateful to the many people who taught us about polynomials and, over many years, have influenced the way we think about the three worlds. It seems hopeless to provide a full accounting of our influences, but in particular we wish to thank Sami Assaf, Alain Lascoux, Cara Monical, Stephanie van Willigenburg, and our common advisor Alexander Yong. We are also thankful for the detailed and helpful comments of two anonymous referees.

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  1. Department of Combinatorics & Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Oliver Pechenik

  2. Department of Mathematics and Statistics, University of Otago, Dunedin, 9016, New Zealand

    Dominic Searles

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  1. Oliver Pechenik
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  2. Dominic Searles
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Correspondence to Oliver Pechenik .

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  1. School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong, China

    Jianxun Hu

  2. School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong, China

    Changzheng Li

  3. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

    Leonardo C. Mihalcea

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Pechenik, O., Searles, D. (2020). Asymmetric Function Theory. In: Hu, J., Li, C., Mihalcea, L.C. (eds) Schubert Calculus and Its Applications in Combinatorics and Representation Theory. ICTSC 2017. Springer Proceedings in Mathematics & Statistics, vol 332. Springer, Singapore. https://doi.org/10.1007/978-981-15-7451-1_5

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