Eulerian polynomials and the 𝑔-indices of Young tableaux

Han, Guo-Niu; Ma, Shi-Mei

doi:10.1090/proc/16650

Eulerian polynomials and the $g$-indices of Young tableaux
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by Guo-Niu Han and Shi-Mei Ma

Proc. Amer. Math. Soc. 152 (2024), 1437-1449

DOI: https://doi.org/10.1090/proc/16650

Published electronically: January 26, 2024

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Abstract:

In this paper, we introduce $k$-Young tableaux and their $g$-indices. We first present certain expansions of $(c(x)D)^n$ in terms of inversion sequences as well as $k$-Young tableaux, where $c(x)$ is a smooth function in the indeterminate $x$ and $D$ is the derivative with respect to $x$. By studying the connections between $k$-Young tableaux and standard Young tableaux, we then present combinatorial interpretations of Eulerian polynomials, second-order Eulerian polynomials, and André polynomials in terms of standard Young tableaux.

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