Gardner et al. posed the problem to find a discrete analogue of Meyer’s inequality bounding from below the volume of a convex body by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated by this problem, for which we provide a first general bound, we study in a more general context the question of bounding the number of lattice points of a convex body in terms of slices, as well as projections.

中文翻译：

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通过切片和投影在格点枚举器上的边界

加德纳等人。提出了一个问题，即通过其切片的体积与坐标超平面的几何平均值，从凸体的体积下方找到 Meyer 不等式的离散模拟。受这个问题的启发，我们为此提供了第一个一般界限，我们在更一般的背景下研究了根据切片和投影对凸体的格点数量进行界定的问题。