On Ehrhart Polynomials of Lattice Triangles

Hofscheier, Johannes; Nill, Benjamin; �berg, Dennis

Abstract

The Ehrhart polynomial of a lattice polygon PP is completely determined by the pair (b(P),i(P))(b(P),i(P)) where b(P)b(P) equals the number of lattice points on the boundary and i(P)i(P) equals the number of interior lattice points. All possible pairs (b(P),i(P))(b(P),i(P)) are completely described by a theorem due to Scott. In this note, we describe the shape of the set of pairs (b(T),i(T))(b(T),i(T)) for lattice triangles TT by finding infinitely many new Scott-type inequalities.

• Journal Article Type: Article
• Acceptance Date: Dec 19, 2017
• Online Publication Date: Jan 12, 2018
• Publication Date: Jan 12, 2018
• Deposit Date: Jul 22, 2020
• Publicly Available Date: Jul 22, 2020
• Journal: The Electronic Journal of Combinatorics
• Print ISSN: 1077-8926
• Publisher: Electronic Journal of Combinatorics
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 1
• DOI: https://doi.org/10.37236/6624
• Keywords: Theoretical Computer Science; Computational Theory and Mathematics; Geometry and Topology
• Public URL: https://nottingham-repository.worktribe.com/output/4782104
• Publisher URL: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p3