Geodesic
A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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.
DOI : 10.37236/243
Classification : 05A19, 11B65, 52A37
Mots-clés : convolution of ultra-logconcave sequences, mixed volumes of convex sets, Minkowski sum, Minkowski polynomial 
@article{10_37236_243,
     author = {Leonid Gurvits},
     title = {A short proof, based on mixed volumes, of {Liggett's} theorem on the convolution of ultra-logconcave sequences},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/243},
     zbl = {1159.05054},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/243/}
}
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Leonid Gurvits. A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/243

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