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- W2898702801 abstract "We give a self-contained proof of the strongest version of Mason's conjecture, namely that for any matroid the sequence of the number of independent sets of given sizes is ultra log-concave. To do this, we introduce a class of polynomials, called completely log-concave polynomials, whose bivariate restrictions have ultra log-concave coefficients. At the heart of our proof we show that for any matroid, the homogenization of the generating polynomial of its independent sets is completely log-concave." @default.
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- W2898702801 date "2018-11-05" @default.
- W2898702801 modified "2023-09-27" @default.
- W2898702801 title "Log-Concave Polynomials III: Mason's Ultra-Log-Concavity Conjecture for Independent Sets of Matroids" @default.
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