4 papers
Irreducible Markov Chains on spaces of graphs with fixed degree-color sequences
Félix Almendra-Hernández, Jesús A. De Loera, Sonja PetroviÄ
We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with co…
Ramsey Numbers through the Lenses of Polynomial Ideals and Nullstellensätze
Jesús A. De Loera, William J. Wesley
In this article we study the Ramsey numbers through Hilbert's Nullstellensatz and Alon's Combinatorial Nullstellensatz. We give polynomial encodings whose solutions corres…
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…
Integer Points in Arbitrary Convex Cones: The Case of the PSD and SOC Cones
Jesús A. De Loera, Brittney Marsters, Luze Xu +1
We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigr…