Nested Log-Concavity

作者：Llamas Aurora; Martinez Bernal Jose^*

来源：Communications in Algebra, 2010, 38(5): 1968-1981.

DOI：10.1080/00927870902950662

• Betti-numbers
• Lexsegment monomial ideal
• Log-concavity

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 epsilon 1; for any polynomial p(x) with positive leading coefficient, there is t0 epsilon 0 such that for any t epsilon t0 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 t0; Betti numbers of lexsegment monomial ideals are strictly log-concave.

• 出版日期2010