On Ehrhart polynomials of lattice triangles
Johannes Hofscheier, Benjamin Nill, Dennis \"Oberg
TL;DR
This paper explores the set of boundary and interior lattice point pairs for lattice triangles, extending Scott's theorem with new inequalities to better understand their geometric properties.
Contribution
It introduces infinitely many new Scott-type inequalities that describe the shape of the set of boundary and interior lattice point pairs for lattice triangles.
Findings
New Scott-type inequalities for lattice triangles
Complete description of the set of (b(T), i(T)) pairs
Enhanced understanding of lattice triangle geometry
Abstract
The Ehrhart polynomial of a lattice polygon P is completely determined by the pair (b(P),i(P)) where b(P) equals the number of lattice points on the boundary and i(P) equals the number of interior lattice points. All possible pairs (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)) for lattice triangles T by finding infinitely many new Scott-type inequalities.
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