A Proof of Grünbaum's Lower Bound Conjecture for general polytopes
Abstract
In 1967, Grünbaum conjectured that any $d$dimensional polytope with $d+s\leq 2d$ vertices has at least \[\phi_k(d+s,d) = {d+1 \choose k+1 }+{d \choose k+1 }{d+1s \choose k+1 } \] $k$faces. We prove this conjecture and also characterize the cases in which equality holds.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.08429
 Bibcode:
 2020arXiv200408429X
 Keywords:

 Mathematics  Combinatorics