A refined lower bound theorem for $d$-polytopes with at most $2d$ vertices

Guillermo Pineda-Villavicencio, Jie Wang, David Yost

In 1967, Grünbaum conjectured that the function $${\varphi }_k(d+s,d):=\left(\genfrac{}{}{0ex}{}{d+1}{k+1}\right)+\left(\genfrac{}{}{0ex}{}{d}{k+1}\right)-\left(\genfrac{}{}{0ex}{}{d+1-s}{k+1}\right),\text{for 2≤s≤d}$$ provides the minimum number of $k$-…