A Proof of Grünbaum’s Lower Bound Conjecture for general polytopes
نویسندگان
چکیده
In 1967, Grünbaum conjectured that any d-dimensional polytope with d + s ? 2d vertices has at least $${\phi _k}(d s,d) = \left( {\matrix{{d 1} \cr {k } \right) {\matrix{d - {\matrix{ {d 1 s} \right)$$ k-faces. We prove this conjecture and also characterize the cases in which equality holds.
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2021
ISSN: ['1565-8511', '0021-2172']
DOI: https://doi.org/10.1007/s11856-021-2234-x