A Proof of Grünbaum's Lower Bound Conjecture for general polytopes

2020/04/17 by Xue, Lei · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.08429

Abstract

In 1967, Grünbaum conjectured that any d-dimensional polytope with d+s≤ 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.

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