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arXiv · 2308.16782

Real-rootedness of the type A minuscule polynomials

Ming-Jian Ding·Jiang Zeng
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Abstract

We prove two recent conjectures of Bourn and Erickson (2023) regarding the real-rootedness of a certain family of polynomials $N_n(t)$ as well as the sum of their coefficients. These polynomials arise as the numerators of generating functions in the context of the discrete one-dimensional earth mover's distance (EMD) and have also connection to the Wiener index of minuscule lattices. We also prove that the coefficients of $N_n(x)$ are asymptotically normal, the coefficient matrix of $N_n(x)$ is totally positive and the polynomial sequence $N_n(x)$'s is $x$-log-concave.

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Ming-Jian Ding, Jiang Zeng. 2024-07-06. Real-rootedness of the type A minuscule polynomials. https://arxiv.org/abs/2308.16782

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