Ultra log-concavity and real-rootedness of dependence polynomials

Yan-Ting Xie, Shou-Jun Xu

For some positive integer $m$, a real polynomial $P(x)=\sum _{k=0}^m{a}_k{x}^k$ with $a_k⩾0$ is called log-concave (resp. ultra log-concave) if $a_k^2\geqslant a_{k-1}a_…