Ehrhart series coefficients for random lattice polytopes
- 1. Imperial College London
- 2. University of Nottingham
Description
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
a positive integer in . - Choose
lattice points uniformly at random in a box , where is chosen uniformly at random in . - Set
. If then return to step 2.
The final dataset has duplicate records removed. The data is distributed by dimension
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
ULID: A randomly generated string identifier for this record.
Dimension: A positive integer. The dimension
Volume: A positive integer. The lattice-normalised volume
EhrhartDelta: A sequence
Ehrhart: A sequence
LogEhrhart: A sequence
Files
dimension.ipynb
Files
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