A triangle {a(n,k)}0≤k≤n of nonnegative numbers is LC-positive
if for each r, the sequence of polynomials ∑k=rna(n,k)qk is
q-log-concave. It is double LC-positive if both triangles {a(n,k)} and
{a(n,n−k)} are LC-positive. We show that if {a(n,k)} is LC-positive
then the log-concavity of the sequence {xk} implies that of the sequence
{zn} defined by zn=∑k=0na(n,k)xk, and if {a(n,k)} is
double LC-positive then the log-concavity of sequences {xk} and {yk}
implies that of the sequence {zn} defined by
zn=∑k=0na(n,k)xkyn−k. Examples of double LC-positive triangles
include the constant triangle and the Pascal triangle. We also give a
generalization of a result of Liggett that is used to prove a conjecture of
Pemantle on characteristics of negative dependence.Comment: 16 page