PreprintCC BY 4.0arXiv
Unbounded log-concavity breaks in independence polynomials of spherically symmetric trees
Abstract
Using a dioid algebraic structure, we show that there exist spherically symmetric trees T(2m 1n) 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].
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BibTeX
@misc{bautistaramos2026unbounded,
title = {{Unbounded log-concavity breaks in independence polynomials of spherically symmetric trees}},
author = {César Bautista-Ramos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04172},
eprint = {2610.04172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04172},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unbounded log-concavity breaks in independence polynomials of spherically symmetric trees
AU - César Bautista-Ramos
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.04172
UR - https://arxiv.org/abs/2610.04172
AB - 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].
ER -