A Short Proof, Based on Mixed Volumes, of Liggett's Theorem on the Convolution of Ultra-Logconcave Sequences
R. Pemantle conjectured, and T.M. Liggett proved in 1997, that the convolution of 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.