Year: 2026
Type: preprint
Abstract: Using a dioid algebraic structure, we show that there exist spherically symmetric trees $T(2^m 1^n)$ whose independence polynomials exhibit multiple breaks in log-concavity, a result established by estimating the asymptotic growth of the coefficients of these polynomials. Provided the parameter $n$ is a sufficiently large odd integer, the number of breaks is bounded below by the Jacobsthal numbers. This result affirmatively answers a question raised by F. Bencs [D. Galvin, Trees with non log-concave independent set sequences, arXiv 2502.10654.v2].
Source: arXiv (Cornell University)
Author: Bautista-Ramos, César
Institution: Benemérita Universidad Autónoma de Puebla
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220691418