Complete Log Concavity of Coverage-Like Functions
Combinatorics
2023-03-08 v1 Discrete Mathematics
Data Structures and Algorithms
Abstract
We introduce an expressive subclass of non-negative almost submodular set functions, called strongly 2-coverage functions which include coverage and (sums of) matroid rank functions, and prove that the homogenization of the generating polynomial of any such function is completely log-concave, taking a step towards characterizing the coefficients of (homogeneous) completely log-concave polynomials. As a consequence we obtain that the "level sets" of any such function form an ultra-log concave sequence.
Cite
@article{arxiv.2303.03741,
title = {Complete Log Concavity of Coverage-Like Functions},
author = {Dorna Abdolazimi and Shayan Oveis Gharan},
journal= {arXiv preprint arXiv:2303.03741},
year = {2023}
}