4 papers
Coloopless zonotopes and counterexamples to the Shifted Lonely Runner Conjecture
Mónica Blanco, Francisco Criado, Francisco Santos
Henze and Malikiosis (2017) have shown that the Lonely Runner Conjecture (LRC) can be restated as a convex-geometric question on the so-called LR zonotopes, lattice zonotopes with…
Covering radii of -zonotopes and the shifted Lonely Runner Conjecture
David Alcántara, Francisco Criado, Francisco Santos
We show that the shifted Lonely Runner Conjecture (sLRC) holds for 5 runners. We also determine that there are exactly 3 primitive tight instances of the conjecture, only two of wh…
On the convex hull of integer points above the hyperbola
David Alcántara, Mónica Blanco, Francisco Criado +1
We show that the polyhedron defined as the convex hull of the lattice points above the hyperbola has between and vertices.…
The algorithmic Fried Potato Problem in two dimensions
Francisco Criado, Francisco Santos
Conway's Fried Potato Problem seeks to determine the best way to cut a convex body in parts by hyperplane cuts (with the restriction that the -th cut only divides in t…