Nested Log-Concavity
Nested Log-Concavity
复制标题
DOI：
10.1080/00927870902950662
复制
发表时间：
2010-04
影响因子：
0.7
通讯作者：
Aurora Llamas;José Martínez-Bernal
中科院分区：
文献类型：
--
作者：
Aurora Llamas;José Martínez-Bernal
给出了多项式系数p(x+t)是对数凹或严格对数凹的条件。给出了几个应用：如果p(X)是系数非负且非递减的多项式，则p(x+t)对所有t≥1是严格对数凹的；对任何具有正前导系数的p(X)，存在t0≥0，使得对任意t≥t0，p(x+t)的系数是正的、严格递减的且严格对数凹的；如果p(X)是非负系数且没有内零点的对数凹多项式，则p(x+t)对所有t>；0严格对数凹；分词单项理想的Betti数是严格对数凹的。
We give conditions on the coefficients of a polynomial p(x) so that p(x + t) be log-concave or strictly log-concave. Several applications are given: if p(x) is a polynomial with nonnegative and nondecreasing coefficients, then p(x + t) is strictly log-concave for all t ≥ 1; for any polynomial p(x) with positive leading coefficient, there is t 0 ≥ 0 such that for any t ≥ t 0 it holds that the coefficients of p(x + t) are positive, strictly decreasing, and strictly log-concave; if p(x) is a log-concave polynomial with nonnegative coefficients and no internal zeros, then p(x + t) is strictly log-concave for all t > 0; Betti numbers of lexsegment monomial ideals are strictly log-concave.