Ehrhart series coefficients for random lattice polytopes
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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:

 1) Fix d a positive integer in {2,...8}.
 2) Choose d + k lattice points {v_1,...,v_(d+k)} uniformly at random in a box [-5,5]^d, where k is chosen uniformly at random in {1,...,5}.
 3) Set P := conv{v_1,...,v_(d+k)}. If dim(P) is not equal to 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
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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
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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 <= d <= 8 of the polytope P.
Volume: A positive integer. The lattice-normalised volume Vol(P) of the polytope P.
EhrhartDelta: A sequence [1,a_1,a_2,...,a_d] of integers of length d + 1. This is the Ehrhart delta-vector (or h*-vector) of P. The Ehrhart series Ehr(P) of P is given by the power-series expansion of (1 + a_1*t + a_2*t^2 + ... + a_d*t^d) / (1 - t)^(d+1). In particular, Vol(P) = 1 + a_1 + a_2 + ... + a_d.
Ehrhart: A sequence [1,c_1,c_2,...,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 Z^d). Equivalently, c_i is the coefficient of t^i in Ehr(P) = 1 + c_1*t + c_2*t^2 + ... = (1 + a_1*t + a_2*t^2 + ... + a_d*t^d) / (1 - t)^(d+1).
LogEhrhart: A sequence [0,y_1,y_2,...,y_1100] of non-negative floating point numbers. Here y_i := log c_i.
