Empty simplices of large width
- Francisco Santos (Universidad de Cantabria)
Abstract
An empty simplex is a lattice simplex in which vertices are the only lattice points. After reviewing what is known about width of lattice polytopes and convex bodies, we show two constructions leading to the first known empty simplices of width larger than their dimension:
(1) We introduce cyclotomic simplices and exhaustively compute all the cyclotomic simplices of dimension
(2) Using circulant matrices of a very specific form, we construct empty simplices of arbitrary dimension
The width in part (2) is (asymptotically) only
This is joint work with Joseph Doolittle, Lukas Katthän, and Benjamin Nill.
