Ehrhart series coefficients for random lattice polytopes

Ehrhart series coefficients for random lattice polytopes A dataset of Ehrhart data for 2918 randomly generated lattice polytopes, in dimensions 2 to 8. The polytopes used to generate this data were produced by the following algorithm: Fix (d) a positive integer in ({2,\ldots,8}). Choose (d + k) lattice points ({v_1,\ldots,v_{d+k}}) uniformly at random in a box ([-5,5]^d), where (k) is chosen uniformly at random in ({1,\ldots,5}). Set (P := \mathrm{conv}{v_1,\ldots,v_{d+k}}). If (\mathrm{dim}(P)\neq d) then return to step 2. The final dataset has duplicate records removed. The data is distributed by dimension (d) as follows: d 2 3 4 5 6 7 8 # 431 787 812 399 181 195 113 For details, see the paper:  Machine Learning the Dimension of a Polytope, Tom Coates, Johannes Hofscheier, and Alexander M. Kasprzyk, 2022. If you make use of this data, please cite the above paper and the DOI for this data:  doi:10.5281/zenodo.6614821 dimension.txt.gz The file "dimension.txt.gz" is a gzip-compressed plain text file containing key:value records with keys and values as described below, where each record is separated by a blank line. There are 2918 records in the file. Example record ULID: 1FTU9VGPXXU82CTDGD6WYMBF9 Dimension: 3 Volume: 342 EhrhartDelta: [1,70,223,48] Ehrhart: [1,74,513,...] LogEhrhart: [0.000000000000000000000000000000,4.30406509320416975378532779249,6.24027584517076953419476314266,...] (The values for Ehrhart and LogEhrhart in the example have been truncated.) For each polytope (P) of dimension (d) we record the following keys and values in the dataset: ULID: A randomly generated string identifier for this record. Dimension: A positive integer. The dimension (2 \leq d \leq 8) of the polytope (P). Volume: A positive integer. The lattice-normalised volume (\mathrm{Vol}(P)) of the polytope (P). EhrhartDelta: A sequence ([1,a_1,a_2,\ldots,a_d]) of integers of length (d + 1). This is the Ehrhart (\delta)-vector (or (h^*)-vector) of (P). The Ehrhart series (\mathrm{Ehr}(P)) of (P) is given by the power-series expansion of ((1 + a_1t + a_2t^2 + \ldots + a_dt^d) / (1 - t)^{d+1}). In particular, (\mathrm{Vol}(P) = 1 + a_1 + a_2 + \ldots + a_d). Ehrhart: A sequence ([1,c_1,c_2,\ldots,c_{1100}]) of positive integers. The value (c_i) is equal to the number of lattice points in the (i)-th dilation of (P), that is, (c_i = #(iP \cap \mathbb{Z}^d)). Equivalently, (c_i) is the coefficient of (t^i) in (\mathrm{Ehr}(P) = 1 + c_1t + c_2t^2 + \ldots = (1 + a_1t + a_2t^2 + \ldots + a_dt^d) / (1 - t)^{d+1}). LogEhrhart: A sequence ([0,y_1,y_2,\ldots,y_{1100}]) of non-negative floating point numbers. Here (y_i := \log c_i)