Fe b 20 06 Log-concavity and LC-positivity

A triangle {a(n, k)}0≤k≤n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials ∑n k=r a(n, k)q k 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… (More)