PreprintCC0arXiv
Preservation of log-concavity under Hadamard products
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.
Related
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BibTeX
@misc{liu2026preservation,
title = {{Preservation of log-concavity under Hadamard products}},
author = {Yanxin Liu and Jianxi Mao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11589},
eprint = {2609.11589},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11589},
note = {CC0},
}
RIS
TY - UNPB
TI - Preservation of log-concavity under Hadamard products
AU - Yanxin Liu
AU - Jianxi Mao
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11589
UR - https://arxiv.org/abs/2609.11589
AB - 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.
ER -