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arXiv · 2609.20961

Unimodality of Independence Polynomials for Sufficiently Large Forests

Ethan X. Fang·Junwei Lu·Eran Nevo·Yuan Yao·Hailun Zheng
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Abstract

We prove that the independence sequence of every sufficiently large forest is unimodal. The result follows from establishing log-concavity on a central interval of the sequence, along with monotonicity of the initial and final segments. The main analytic step is a central limit theorem for the size of a random independent set sampled with the hard-core model, uniform over all forests and over an interval of positive fugacities.

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Ethan X. Fang, Junwei Lu, Eran Nevo, Yuan Yao, Hailun Zheng. 2026-09-17. Unimodality of Independence Polynomials for Sufficiently Large Forests. https://arxiv.org/abs/2609.20961

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