2 papers
math.CO2020
A Proof of Grünbaum's Lower Bound Conjecture for general polytopes
Lei Xue
In 1967, Grünbaum conjectured that any -dimensional polytope with vertices has at least \[ϕ_k(d+s,d) = {d+1 \choose k+1 }+{d \choose k+1 }-{d+1-s \choose k+1 } \] $…
math.CO2020
Non-Eulerian Dehn-Sommerville relations
Connor Sawaske, Lei Xue
The classical Dehn--Sommerville relations assert that the -vector of an Eulerian simplicial complex is symmetric. We establish three generalizations of the Dehn--Sommerville rel…