论文标题
抗块机器的几何不平等现象
Geometric Inequalities for Anti-Blocking Bodies
论文作者
论文摘要
我们研究（本地）抗块体的类别以及一些相关的凸体类。对于这些身体，我们证明了有关体积和混合体积的几何不平等，包括戈伯森的猜想，在Mahler体积上的近乎最佳界限，混合体积上的Saint-Raymond-type不平等，以及混合体积的反向Kleitman不平等。我们将结果应用于POSET的组合，并证明了侧龙型的不等式的不等式，这是二维POSET对的线性扩展。结果依赖于抗震动体差异的一些优雅分解，这些分解与一般的多面体锥相对于抗块体而言，这些分解可容纳抗块体。
We study the class of (locally) anti-blocking bodies as well as some associated classes of convex bodies. For these bodies, we prove geometric inequalities regarding volumes and mixed volumes, including Godberson's conjecture, near-optimal bounds on Mahler volumes, Saint-Raymond-type inequalities on mixed volumes, and reverse Kleitman inequalities for mixed volumes. We apply our results to the combinatorics of posets and prove Sidorenko-type inequalities for linear extensions of pairs of 2-dimensional posets. The results rely on some elegant decompositions of differences of anti-blocking bodies, which turn out to hold for anti-blocking bodies with respect to general polyhedral cones.
