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

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

2008-04-08

arxiv.org/abs/0804.1181v1

Mathematics

Combinatorics

4 pages; short and easy

Scientific paper

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.

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