We consider geometric and computational measures of complexity for sets of integer vectors, asking for a qualitative difference between $f$-vectors of simplicial and general $d$-polytopes, as well as flag $f$-vectors of $d$-polytopes and regular CW $(d-1)$-spheres, for $d\ge 4$.

中文翻译：

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多面体和球体 f 向量的复杂度标准

我们考虑整数向量集的复杂性的几何和计算度量，要求 $f$-vectors of simplicial 和一般 $d$-polytopes 以及标志 $f$-vectors of $d$-polytopes 之间存在质的差异和常规 CW $(d-1)$-spheres，$d\ge 4$。