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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- 1.
\(C_n\equiv \left( {\begin{array}{c}2n\\ n\end{array}}\right) \frac{1}{n+1}\).
- 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.
Recall \(\lambda \le \mu \) means that \(\lambda _i\le \mu _i\) for all i.
- 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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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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