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Lattice 3-Polytopes with Few Lattice Points

Abstract: We extend White's classification of empty tetrahedra to the complete classification of lattice 3-polytopes with five lattice points, showing that, apart from infinitely many of width one, there are exactly nine equivalence classes of them with width two and none of larger width. We also prove that, for each $n\in\mathbb{N}$, there is only a finite number of (classes of) lattice 3-polytopes with $n$ lattice points and of width larger than one. This implies that extending the present classification to larger sizes makes sense, which is the topic of subsequent papers of ours.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: SIAM J. Discrete Math., 30(2), 669-686.

Editorial: Society for Industrial and Applied Mathematics

 Año de publicación: 2016

Nº de páginas: 17

Tipo de publicación: Artículo de Revista

 DOI: 10.1137/15M1014450

ISSN: 0895-4801,1095-7146

Proyecto español: BES-2012-058920

Url de la publicación: https://doi.org/10.1137/15M1014450