A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences (Q1010896)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences |
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A short proof, based on mixed volumes, of Liggett's theorem on the convolution of ultra-logconcave sequences (English)
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7 April 2009
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Summary: R. Pemantle conjectured, and \textit{T.M. Liggett} proved in J. Comb. Theory, Ser. A 79, No.\,2, 315--325 (1997; Zbl 0888.60013), 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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convolution of ultra-logconcave sequences
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mixed volumes of convex sets
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Minkowski sum
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Minkowski polynomial
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