Classification of Width 1 Lattice Tetrahedra by Their Multi-Width

Hamm, Girtrude

Abstract

We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width (1,w2,w3). 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,w2,w3) for small w2 and w3 and make conjectures about the function counting lattice tetrahedra of any multi-width.

Citation

Hamm, G. (2024). Classification of Width 1 Lattice Tetrahedra by Their Multi-Width. Discrete and Computational Geometry, https://doi.org/10.1007/s00454-024-00659-5

• Journal Article Type: Article
• Acceptance Date: May 5, 2024
• Online Publication Date: Jun 4, 2024
• Publication Date: 2024
• Deposit Date: Jun 6, 2024
• Publicly Available Date: Jun 6, 2024
• Journal: Discrete and Computational Geometry
• Print ISSN: 0179-5376
• Electronic ISSN: 1432-0444
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1007/s00454-024-00659-5
• Keywords: Lattice polytope; Multi-width; Simplex; Classification algorithm
• Public URL: https://nottingham-repository.worktribe.com/output/35730708
• Publisher URL: https://link.springer.com/article/10.1007/s00454-024-00659-5