2023/04/06 by Girtrude Hamm, Hamm, Girtrude · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2304.03007
openalex publication_date 2023/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of the second lattice width of a lattice polytope and use this to classify lattice triangles by their width and second width. This is equivalent to classifying lattice triangles contained in a given rectangle (and no smaller rectangle) up to affine equivalence. Using this classification we investigate the automorphism groups and Ehrhart theory of lattice triangles. We also show that the sequence counting lattice triangles contained in dilations of the unit square has generating function equal to the Hilbert series of a degree 8 hypersurface in ℙ(1,1,1,2,2,2).