منابع مشابه
Infinite log-concavity: developments and conjectures
Given a sequence (ak) = a0, a1, a2, . . . of real numbers, define a new sequence L(ak) = (bk) where bk = ak − ak−1ak+1. So (ak) is log-concave if and only if (bk) is a nonnegative sequence. Call (ak) infinitely log-concave if L(ak) is nonnegative for all i ≥ 1. Boros and Moll [3] conjectured that the rows of Pascal’s triangle are infinitely log-concave. Using a computer and a stronger version o...
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This is a small observation concerning scale mixtures and their log-concavity. A function f(x) ≥ 0, x ∈ Rn is called log-concave if f (λx + (1− λ)y) ≥ f(x)f(y) (1) for all x,y ∈ Rn, λ ∈ [0, 1]. Log-concavity is important in applied Bayesian Statistics, since a distribution with a log-concave density is easy to treat with many different approximate inference techniques. For example, log-concavit...
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We show that f -vectors of matroid complexes of realizable matroids are strictly log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who showed that the coefficients of the characteristic polynomial of a realizable matroid form a log-concave sequence. We also prove a statement on log-concavity of h-vectors which strengthens a result by Brown and ...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2015
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-015-0292-7