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arXiv · 2609.11589

Preservation of log-concavity under Hadamard products

Yanxin Liu·Jianxi Mao
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Abstract

For a nonzero real polynomial $p$, let $\W(p)$ denote the numerator of its ordinary generating function. We prove that if the coefficients of both $\W(p)$ and $\W(q)$ are nonnegative and log-concave with no internal zeros, then so are the coefficients of $\W(pq)$. This provides an affirmative answer to a question of Brändén, Ferroni, and Jochemko. As applications, we derive corresponding results for finite products and for Cartesian products of lattice polytopes, answering a question of Ferroni and Higashitani.

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Yanxin Liu, Jianxi Mao. 2026-09-10. Preservation of log-concavity under Hadamard products. https://arxiv.org/abs/2609.11589

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