A short, based on the mixed volume, proof of Liggett's theorem on the convolution of ultra-logconcave sequences
Combinatorics
2008-04-10 v1 Statistics Theory
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0804.1181,
title = {A short, based on the mixed volume, proof of Liggett's theorem on the convolution of ultra-logconcave sequences},
author = {Leonid Gurvits},
journal= {arXiv preprint arXiv:0804.1181},
year = {2008}
}
Comments
4 pages; short and easy