Brunn-minkowski Inequalities for Contingency Tables and Integer Flows
نویسنده
چکیده
We establish approximate log-concavity for a wide family of combinatorially defined integer-valued functions. Examples include the number of non-negative integer matrices (contingency tables) with prescribed row and column sums (margins), as a function of the margins and the number of integer feasible flows in a network, as a function of the excesses at the vertices. As a corollary, we obtain approximate log-concavity for the Kostant partition function of type A. We also present an indirect evidence that at least some of the considered functions might be genuinely log-concave.
منابع مشابه
Volume difference inequalities for the projection and intersection bodies
In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.
متن کاملVolume Inequalities and Additive Maps of Convex Bodies
Analogs of the classical inequalities from the Brunn Minkowski Theory for rotation intertwining additive maps of convex bodies are developed. We also prove analogs of inequalities from the dual Brunn Minkowski Theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary we obtain a new Brunn Mi...
متن کاملThe Infinitesimal Form of Brunn-minkowski Type Inequalities
Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang [7], and it states that a certain strengthening of the classical Brunn-Minkowski inequality is admissible in the case of symmetric convex sets. It was recently shown by Nayar, Zvavitch, the second and the third authors [27], that Log-Brunn-Minkowski inequality implies a certain dimensional Brunn-Minkowski inequal...
متن کاملStar Valuations and Dual Mixed Volumes
Since its creation by Brunn and Minkowski, what has become known as the Brunn Minkowski theory has provided powerful machinery to solve a broad variety of inverse problems with stereological data. The machinery of the Brunn Minkowski theory includes mixed volumes (of Minkowski), symmetrization techniques (such as those of Steiner and Blaschke), isoperimetric inequalities (such as the Brunn Mink...
متن کاملOn the Orlicz-Brunn-Minkowski theory
Recently, Gardner, Hug and Weil developed an Orlicz-Brunn1 Minkowski theory. Following this, in the paper we further consider the 2 Orlicz-Brunn-Minkowski theory. The fundamental notions of mixed quer3 massintegrals, mixed p-quermassintegrals and inequalities are extended to 4 an Orlicz setting. Inequalities of Orlicz Minkowski and Brunn-Minkowski 5 type for Orlicz mixed quermassintegrals are o...
متن کامل