Classification of width 1 lattice tetrahedra by their multi-width

Girtrude Hamm

doi:10.1007/s00454-024-00659-5

paper

Classification of width 1 lattice tetrahedra by their multi-width

arXiv:2304.03627 · doi:10.1007/s00454-024-00659-5

Abstract

We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width $(1, w_{2}, w_{3})$ . The approach used in this classification can be extended into a computer algorithm to classify lattice tetrahedra of any given multi-width. We use this to classify tetrahedra with multi-width $(2, w_{2}, w_{3})$ for small $w_{2}$ and $w_{3}$ and make conjectures about the function counting lattice tetrahedra of any multi-width.

21 pages, 4 figures