64 citations · 418 across the 52 of their papers we have counts for
6 papers · 1 filter
On Unavoidable Faces of High-Dimensional Polytopes
Jesús A. De Loera, Ethan X. Fang, Shengtao Guo +2
Kalai's cube--simplex conjecture asserts that for all positive integers , there is an integer such that every polytope of dimension at least has eit…
Sharp Bounds on the Independence Number of Simplicial Spheres
Jesús A. De Loera, Ethan X. Fang, Junwei Lu +2
We study the maximum size of an independent set in the graph of a simplicial sphere. Let denote this maximum over all simplicial -spheres on vertices, and let $…
From Ham-Sandwich to Centerpoints: Semialgebraic Algorithms for Cutting Polytopal Measures
Marie-Charlotte Brandenburg, Jesús A. De Loera, Chiara Meroni
We design exact algorithms for the ham-sandwich and centerpoint theorems for polytopal measures. Our key observation is that the cap-volume function of such a measure, i.e., the vo…
Persistent Subdivisions of Coxeter Permutahedra
Timothy Blanton, Jesús A. De Loera, Melissa Sherman-Bennett
We investigate the realizations of Coxeter permutahedra which are also Coxeter matroid polytopes; these are polytopes of the form where is a…
There are matroid toric ideals without quadratic Gröbner bases
Jesús A. De Loera, Luis Ferroni, Santiago Morales +1
Our paper shows that if a matroid contains the Fano plane or its dual as a minor, then its toric ideal does not have any quadratic Gröbner basis. More than 25 years ago, Hibi, Herz…
Critical moments of slices and slabs of the cube (and other polyhedral norms)
Marie-Charlotte Brandenburg, Jesús A. De Loera, Yu Luo +1
In this article, we present a unified algebraic-combinatorial framework for computing explicit, piecewise rational, and combinatorially indexed parametric formulas for volumes and…