In 1967, Grünbaum conjectured that any $d$-dimensional polytope with $d+s\leq 2d$ vertices has at least \[φ_k(d+s,d) = {d+1 \choose k+1 }+{d \choose k+1 }-{d+1-s \choose k+1 } \] $k$-faces. We prove this conjecture and also characterize the cases in which equality holds.
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。