A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences

摘要

R. Pemantle conjectured, and T. M. Liggett proved in 1997, that the convolutionof two ultra-logconcave is ultra-logconcave. Liggett's proof is elementary but long.We present here a short proof, based on the mixed volume of convex sets.