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math.CO2008
On multivariate Newton-like inequalities
Leonid Gurvits
We study multivariate entire functions and polynomials with non-negative coefficients. A class of {\bf Strongly Log-Concave} entire functions, generalizing {\it Minkowski} volume p…
math.CO2008
A short, based on the mixed volume, proof of Liggett's theorem on the convolution of ultra-logconcave sequences
Leonid Gurvits
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…