We prove an upper bound of the form \(2^{O(d^2 \mathop {\mathrm {polylog}}d)}\) on the number of affine (resp. linear) equivalence classes of, by increasing order of generality, 2-level d-polytopes, d-cones, and d-configurations. This in particular answers positively a conjecture of Bohn et al. on 2-level polytopes. We obtain our upper bound by relating affine (resp. linear) equivalence classes of 2-level d-polytopes, d-cones, and d-configurations to faces of the correlation cone. We complement this with a \(2^{\varOmega (d^2)}\) lower bound, by estimating the number of nonequivalent stable set polytopes of bipartite graphs.

我们证明仿射（分别是线性）等价类的数量，通过增加以下形式的阶数\（2 ^ {O（d ^ 2 \ mathop {\ mathrm {polylog}} d）} \）的上限通用性，2级d-多边形，d-圆锥和d-配置。这尤其肯定地回答了Bohn等人的猜想。在2级多面体上。我们通过将2级d-多边形，d-圆锥和d-构型的仿射（或线性）等价类与相关锥的面相关联来获得上限。通过估计二分图的非等价稳定集多边形的数目，我们用\（2 ^ {\ varOmega（d ^ 2）} \）下界进行补充。