Polygons with small denominator containing a small number of lattice points

<p>The denominator of a rational polytope \(P\) is an integer \(r\) such that the dilated polytope \(rP\) has lattice point vertices. The size of a polytope is the number of lattice points it contains. This dataset contains polygons with denominator 2 and 3 with small size, classified using a growing algorithm as described in [HHK24].</p> <p>The data consists of files "denom_r_size_k_polygons.txt" which record the denominator \(r\) size \(k\) polygons \(P\). Each entry consists of the vertices and volume of \(rP\), the Ehrhart \(\delta\)-vector/\(h^*\)-vector of \(P\), and an ID number, which is unique among polygons of given size and denominator. Entries are ordered by their ID number. There are 50,564 entries in total.</p> <p><strong>Example entry:</strong></p> <p>ID=1<br>Vertices=[[ 1, 0 ], [ 0, 1 ], [ 3, 5 ]]<br>Volume=7<br>DeltaVec=[ 1, 0, 3, 7, 3, 0 ]</p> <p>If you make use of this data, please cite [HHK24] and the DOI for this data:</p> <p>doi:10.5281/zenodo.14230584</p> <p><strong>References:</strong></p> <p>[HHK24] Girtrude Hamm, Johannes Hofscheier, Alexander Kasprzyk, Classification and Ehrhart Theory of Denominator 2 Polygons. (preprint) arxiv:2411.19183</p>