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From Boxes to Polynomials: A Story of Generalization

  • Mathematical Gems and Curiosities
  • Edited by Sophie Morier-Genoud and Valentin Ovsienko
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Notes

  1. For the interested reader, this notation is inspired by the connection between the box combinatorics studied here and the representation theory of the affine Lie algebra, in which K is the canonical central element and \(\alpha _{ij}\) is the difference between two affine coroots.

References

  1. J. Haglund. The \(q,t\)-Catalan Numbers and the Space of Diagonal Harmonics. American Mathematical Society, 2008. https://doi.org/10.1007/s10711-008-9270-0.

  2. I. Macdonald. A New Class of Symmetric Functions. Publ. I.R.M.A. Strasbourg, 372/S20, Actes 20 Séminaire Lotharingien (1988), 131–171.

  3. I. Macdonald. Symmetric Functions and Hall Polynomials. Oxford University Press, 1995.

  4. I. Macdonald. Symmetric Functions and Orthogonal Polynomials. American Mathematical Society, 1998. https://doi.org/10.1090/ulect/012.

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  6. B. Sagan. Combinatorics: The Art of Counting. American Mathematical Society, 2020.

  7. R. Stanley. Enumerative Combinatorics, Vol. 2. Cambridge University Press, 1999. https://doi.org/10.1017/CBO9780511609589.

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Acknowledgments

We would like to express our deepest thanks to Professor Arun Ram for introducing us to the interesting topics of Young tableaux and Macdonald polynomials and for his patience and generosity in guiding three unsuspecting undergraduate students through their first article.

All three of us would also like to thank one another for the useful discussions and the team spirit of helping each other throughout the process. The enthusiasm for mathematics from each of us inspires the whole group to keep doing math with enjoyment.

Finally, we would like to thank Peter Forrester, David Ridout, and the referees for their valuable comments and suggestions in the revision process of the article.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, Australia

    Gypsy Akhyar, Yifan Guo & Lihexuan Yuan

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  1. Gypsy Akhyar
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  2. Yifan Guo
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Correspondence to Lihexuan Yuan.

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Akhyar, G., Guo, Y. & Yuan, L. From Boxes to Polynomials: A Story of Generalization. Math Intelligencer 46, 78–84 (2024). https://doi.org/10.1007/s00283-022-10230-w

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