6 citations · 9 across the 7 of their papers we have counts for
7 papers
Any Proof of Polynomial Hirsch Must be Completely Incoherent
Alexander E. Black, Lei Xue
In 1992, Billera and Sturmfels introduced coherent monotone paths on polytopes as part of their description of the fiber polytope construction, and later in 1994 showed with Kapran…
Topology of Cut Complexes II
Margaret Bayer, Mark Denker, Marija Jelić Milutinović +2
We continue the study of the -cut complex of a graph initiated in the paper of Bayer, Denker, Jelić Milutinović, Rowlands, Sundaram and Xue [Topology of cut complex…
Topology of Cut Complexes of Graphs
Margaret Bayer, Mark Denker, Marija Jelić Milutinović +3
We define the -cut complex of a graph with vertex set to be the simplicial complex whose facets are the complements of sets of size in inducing disconnecte…
Total Cut Complexes of Graphs
Margaret Bayer, Mark Denker, Marija Jelić Milutinović +3
Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the \emph{total -cut complex} of a graph to be the simplicial complex whose facets are the complem…
A Lower Bound Theorem for strongly regular CW spheres with up to vertices
Lei Xue
In 1967, Grünmbaum conjectured that any -dimensional polytope with vertices has at least \[ϕ_k(d+s,d) = {d+1 \choose k+1 }+{d \choose k+1 }-{d+1-s \choose k+1 } \]…
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 \[ϕ_k(d+s,d) = {d+1 \choose k+1 }+{d \choose k+1 }-{d+1-s \choose k+1 } \] $…
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…