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arXiv · 1605.02298

On the real-rootedness of the local $h$-polynomials of edgewise subdivisions

Philip B. Zhang
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Abstract

Athanasiadis conjectured that, for every positive integer $r$, the local $h$-polynomial of the $r$th edgewise subdivision of any simplex has only real zeros. In this paper, based on the theory of interlacing polynomials, we prove that a family of polynomials related to the desired local $h$-polynomial is interlacing and hence confirm Athanasiadis' conjecture.

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Philip B. Zhang. 2019-03-01. On the real-rootedness of the local $h$-polynomials of edgewise subdivisions. https://arxiv.org/abs/1605.02298

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