Work

Unimodality of Independence Polynomials for Sufficiently Large Forests

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.20961

Authors: Fang, Ethan X., Lu, Junwei, Nevo, Eran, Yao, Yuan, Zheng, Hailun

Institutions: Duke University, Universidad de Valladolid, Harvard University, Hebrew University of Jerusalem, University of Hawaiʻi at Mānoa

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213893202

Cites: 4

Cited by: 3

Related to: 10