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.
@article{10_37236_6624,
author = {Johannes Hofscheier and Benjamin Nill and Dennis \"Oberg},
title = {On {Ehrhart} polynomials of lattice triangles},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/6624},
zbl = {1386.52012},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6624/}
}
TY - JOUR
AU - Johannes Hofscheier
AU - Benjamin Nill
AU - Dennis Öberg
TI - On Ehrhart polynomials of lattice triangles
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6624/
DO - 10.37236/6624
ID - 10_37236_6624
ER -
%0 Journal Article
%A Johannes Hofscheier
%A Benjamin Nill
%A Dennis Öberg
%T On Ehrhart polynomials of lattice triangles
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6624/
%R 10.37236/6624
%F 10_37236_6624
Johannes Hofscheier; Benjamin Nill; Dennis Öberg. On Ehrhart polynomials of lattice triangles. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6624
