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On Standard Young Tableaux of Bounded Height

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Recent Trends in Algebraic Combinatorics

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

Abstract

We survey some recent works on standard Young tableaux of bounded height. We focus on consequences resulting from numerous bijections to lattice walks in Weyl chambers.

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Notes

  1. 1.

    \(C_n\equiv \left( {\begin{array}{c}2n\\ n\end{array}}\right) \frac{1}{n+1}\).

  2. 2.

    For convenience we define the chambers using non-strict inequalities, our bijective statements can equivalently be given under strict inequalities, upon applying the coordinate shift \(\widetilde{x}_i=x_i+d+1-i\).

  3. 3.

    Recall \(\lambda \le \mu \) means that \(\lambda _i\le \mu _i\) for all i.

  4. 4.

    A (multivariate) function is D-finite if the set of all its partial derivatives spans a vector space of finite dimension.

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Acknowledgements

The author is grateful to MSRI for travel support to participate in the 2017 AWM session. This expository work was inspired by that meeting. I am grateful for the patience and wisdom of the anonymous referees. The author’s research is also partially funded by NSERC Discovery Grant RGPIN-04157.

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S5, Canada

    M. J. Mishna

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Correspondence to M. J. Mishna .

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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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Mishna, M.J. (2019). On Standard Young Tableaux of Bounded Height. 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_8

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