51 citations · 154 across the 31 of their papers we have counts for
19 papers · 1 filter
On the Number of Vertices in a Hyperplane Section of a Polytope
Jesús A. De Loera, Gyivan Lopez-Campos, Antonio J. Torres
We study the slices or sections of a convex polytope by affine hyperplanes. We present results on two key problems: First, we provide tight bounds on the maximum number of vertices…
Rado Numbers and SAT Computations
Yuan Chang, Jesús A. De Loera, William J. Wesley
Given a linear equation , the -color Rado number is the smallest integer such that every -coloring of contains a monoc…
Monotone Paths on Cross-Polytopes
Alexander Black, Jesús De Loera
In the early 1990's, Billera and Sturmfels introduced the monotone path polytope (MPP), a special case of the general theory of fiber polytopes that associates a polytope to a pair…
Diameters of Cocircuit Graphs of Oriented Matroids: An Update
Ilan Adler, Jesús A. De Loera, Steven Klee +1
Oriented matroids (often called order types) are combinatorial structures that generalize point configurations, vector configurations, hyperplane arrangements, polyhedra, linear pr…
The lattice of cycles of an undirected graph
Gennadiy Averkov, Anastasia Chavez, Jesus A. De Loera +1
We study bases of the lattice generated by the cycles of an undirected graph, defined as the integer linear combinations of the 0/1-incidence vectors of cycles. We prove structural…
Enumerative problems for arborescences and monotone paths on polytope graphs
Christos Athanasiadis, Jesús De Loera, Zhenyang Zhang
Every generic linear functional on a convex polytope induces an orientation on the graph of . From the resulting directed graph one can define a notion of -arborescen…