Classification of Width 1 Lattice Tetrahedra by Their Multi-Width

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2024年6月4日

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Girtrude Hamm

摘要

We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width $(1,w_2,w_3)$ $(1, w_{2}, w_{3})$ . 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 $(2,w_2,w_3)$ $(2, w_{2}, w_{3})$ for small $w_2$ $w_{2}$ and $w_3$ $w_{3}$ and make conjectures about the function counting lattice tetrahedra of any multi-width.