cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.7910/dvn/v81w2r
title: A04_14096.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/6a3d9036-2834-e63c-b7d6-964ae1c184ce'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/6a3d9036-2834-e63c-b7d6-964ae1c184ce
DOI: 10.7910/dvn/lsbf0l
title: A04_14097.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/52334d79-ae74-59db-dfbc-8bd9ebee8279'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/52334d79-ae74-59db-dfbc-8bd9ebee8279
DOI: 10.7910/dvn/6ggtsg
title: A04_14098.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/a69bba1c-303a-6a4a-cd5a-a4fc593d62af'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/a69bba1c-303a-6a4a-cd5a-a4fc593d62af
DOI: 10.7910/dvn/qtd8ga
title: A04_14099a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/1250b9ee-a86c-a61b-1d7c-ba60633c4c66'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/1250b9ee-a86c-a61b-1d7c-ba60633c4c66
DOI: 10.7910/dvn/80ezjh
title: A04_14099b.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/b0ce74c0-2a26-32ae-7c58-8a3ef3afa20b'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/b0ce74c0-2a26-32ae-7c58-8a3ef3afa20b
DOI: 10.7910/dvn/liwnix
title: A04_14100.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/2a31e061-12e6-3b15-2ca6-394828c23933'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/2a31e061-12e6-3b15-2ca6-394828c23933
DOI: 10.7910/dvn/k7l4qs
title: A04_14100a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/41607dbc-1a05-d0d3-7cdb-c35ca6c8c6ea'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/41607dbc-1a05-d0d3-7cdb-c35ca6c8c6ea
DOI: 10.7910/dvn/xakqqi
title: A04_14101.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/4e3df914-d489-b822-8ad8-4c27f88ebc8b'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/4e3df914-d489-b822-8ad8-4c27f88ebc8b
DOI: 10.7910/dvn/vh0nnd
title: A04_14101a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/5bf9d9da-e74e-4135-8f53-14baaaca2ad1'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/5bf9d9da-e74e-4135-8f53-14baaaca2ad1
DOI: 10.7910/dvn/devjqt
title: A04_14102.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/db087c44-75bf-eb6d-07e9-f47df1c6c87f'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/db087c44-75bf-eb6d-07e9-f47df1c6c87f
DOI: 10.7910/dvn/lt5kbz
title: A04_14102a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/c90d4540-dc4d-29fd-7299-db906383b798'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/c90d4540-dc4d-29fd-7299-db906383b798
DOI: 10.7910/dvn/xw4wah
title: A04_14103.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/4109b4da-f142-6f99-ae79-913a4b224625'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/4109b4da-f142-6f99-ae79-913a4b224625
DOI: 10.7910/dvn/fo08j5
title: A04_14103a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/3f5169e8-3853-4571-fcf3-17bca3298a26'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/3f5169e8-3853-4571-fcf3-17bca3298a26
DOI: 10.7910/dvn/j3aoz8
title: A04_14104.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/62b8f9b8-fc89-7247-9484-8cea114f2522'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/62b8f9b8-fc89-7247-9484-8cea114f2522
DOI: 10.7910/dvn/l9e90z
title: A04_14104a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/ca120f0e-8830-d490-edf1-267a72c0f208'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/ca120f0e-8830-d490-edf1-267a72c0f208
DOI: 10.7910/dvn/ipxdoy
title: A04_14105a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/8b552694-f34b-2935-380d-5fe732d9b767'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/8b552694-f34b-2935-380d-5fe732d9b767
DOI: 10.7910/dvn/muetrj
title: A04_14105b.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/4b9fcceb-6ee1-a280-19b2-14dfc1d01db4'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/4b9fcceb-6ee1-a280-19b2-14dfc1d01db4
DOI: 10.7910/dvn/aptqqb
title: A04_14106a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/cc5a109c-4e16-c4d1-2331-b558e766bbc6'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/cc5a109c-4e16-c4d1-2331-b558e766bbc6
DOI: 10.7910/dvn/vk2puo
title: A04_14107.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/61a4a851-6197-e179-67f7-06372db1f3a5'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/61a4a851-6197-e179-67f7-06372db1f3a5
DOI: 10.7910/dvn/m2whg2
title: A04_14107a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/2778beac-4aca-143e-5744-f93edba655b3'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/2778beac-4aca-143e-5744-f93edba655b3
DOI: 10.7910/dvn/td3sk1
title: A04_14108a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/9cc7addf-8e5d-fd23-5a9a-edfd3a6667ea'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/9cc7addf-8e5d-fd23-5a9a-edfd3a6667ea
DOI: 10.7910/dvn/daglzn
title: A04_14110.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/c507e915-5c36-fe7e-9c6a-832ff28a6821'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/c507e915-5c36-fe7e-9c6a-832ff28a6821
DOI: 10.7910/dvn/t5cfl4
title: A04_14111.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/2c7f28c5-6a59-db57-af75-2dc7a3333cd8'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/2c7f28c5-6a59-db57-af75-2dc7a3333cd8
DOI: 10.5281/zenodo.13839215
title: Rational polygons with exactly one interior lattice point

description: This record contains



maximal \(k\)-rational polygons with exactly one interior lattice point for \(1 \leq k \leq 10\),

all \(k\)-rational polygons with exactly one interior lattice point for \(1 \leq k \leq 4\),

all Ehrhart quasipolynomials of these polygons for \(1 \leq k \leq 5\).

all \(k\)-rational LDP polygons (=almost \(k\)-hollow LDP polygons) for \(1 \leq k \leq 5\).


The maximal polygons are stored as text files with one polygon per line. Each line contains the vertices of the polygon multiplied by \(k\) (so that they are integral). The other polygons as well as the Ehrhart quasipolynomials are stored using the HDF5 file format. All polygons and Ehrhart quasipolynomials have been obtained using RationalPolygons.jl.

Structure of the HDF5 files for polygons

In the HDF5 files "all_k<k>.h5", the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the \(3\)-rational polygons with normalized area \(30\) having \(5\) vertices are located in "k3_all.h5" under the dataset "/a30/n5". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon multiplied by \(k\), stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((k\cdot x_1,k\cdot y_1,k \cdot x_2,k\cdot y_2,k \cdot x_3,k \cdot y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.

Structure of the HDF5 files for Ehrhart quasipolynomials

In the HDF5 files "ehrhart_k<k>.h5", the Ehrhart quasipolynomials are split into different datasets according to the normalized area of the associated polygon. We use "a" for the normalized area (twice the euclidian area). For example, the Ehrhart quasipolynomials of all \(3\)-rational polygons with normalized area \(30\) are located in "ehrhart_k3.h5" under the dataset "/a30". Each Ehrhart quasipolynomial is stored as a \(3 \times k\) integral matrix. Hence each dataset is three-dimensional, with the first dimension to enumerate the quasipolynomials and the latter two dimensions to store each quasipolynomial itself. For the way Ehrhart quasipolynomials are encoded as \(3 \times k\) integral matrices, we refer to the relevant documentation of RationalPolygons.jl.
DOI: 10.5281/zenodo.13839216
title: Rational polygons with exactly one interior lattice point

description: This record contains



maximal \(k\)-rational polygons with exactly one interior lattice point for \(1 \leq k \leq 10\),

all \(k\)-rational polygons with exactly one interior lattice point for \(1 \leq k \leq 4\),

all Ehrhart quasipolynomials of these polygons for \(1 \leq k \leq 5\).

all \(k\)-rational LDP polygons (=almost \(k\)-hollow LDP polygons) for \(1 \leq k \leq 5\).


The maximal polygons are stored as text files with one polygon per line. Each line contains the vertices of the polygon multiplied by \(k\) (so that they are integral). The other polygons as well as the Ehrhart quasipolynomials are stored using the HDF5 file format. All polygons and Ehrhart quasipolynomials have been obtained using RationalPolygons.jl.

Structure of the HDF5 files for polygons

In the HDF5 files "all_k<k>.h5", the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the \(3\)-rational polygons with normalized area \(30\) having \(5\) vertices are located in "k3_all.h5" under the dataset "/a30/n5". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon multiplied by \(k\), stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((k\cdot x_1,k\cdot y_1,k \cdot x_2,k\cdot y_2,k \cdot x_3,k \cdot y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.

Structure of the HDF5 files for Ehrhart quasipolynomials

In the HDF5 files "ehrhart_k<k>.h5", the Ehrhart quasipolynomials are split into different datasets according to the normalized area of the associated polygon. We use "a" for the normalized area (twice the euclidian area). For example, the Ehrhart quasipolynomials of all \(3\)-rational polygons with normalized area \(30\) are located in "ehrhart_k3.h5" under the dataset "/a30". Each Ehrhart quasipolynomial is stored as a \(3 \times k\) integral matrix. Hence each dataset is three-dimensional, with the first dimension to enumerate the quasipolynomials and the latter two dimensions to store each quasipolynomial itself. For the way Ehrhart quasipolynomials are encoded as \(3 \times k\) integral matrices, we refer to the relevant documentation of RationalPolygons.jl.
DOI: 10.7910/dvn/rt6l2z
title: A04_14112a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/e87c21af-9746-320e-5262-cdd46eee7d07'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/e87c21af-9746-320e-5262-cdd46eee7d07
DOI: 10.7910/dvn/bh0flg
title: A04_14113.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/2aa1befc-112e-f861-228c-93d95290ff57'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/2aa1befc-112e-f861-228c-93d95290ff57
DOI: 10.7910/dvn/udfttd
title: A04_14113a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/49084600-11ff-01c4-7e5c-5680ef6bd738'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/49084600-11ff-01c4-7e5c-5680ef6bd738
DOI: 10.7910/dvn/liddqq
title: A04_14114.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/ce17014e-37b3-ef2a-233c-86bdc51ab638'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/ce17014e-37b3-ef2a-233c-86bdc51ab638
DOI: 10.7910/dvn/ccbave
title: A04_14115.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/a65c432d-c19b-b5e8-3060-d44845c07bdf'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/a65c432d-c19b-b5e8-3060-d44845c07bdf
DOI: 10.7910/dvn/q5shwm
title: A04_14116.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/135f0b15-4925-f75d-2e5f-c1a35639b5c1'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/135f0b15-4925-f75d-2e5f-c1a35639b5c1
DOI: 10.7910/dvn/carqas
title: A04_14116a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/e17aa478-744e-b776-8389-cc5e37be0b1f'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/e17aa478-744e-b776-8389-cc5e37be0b1f
DOI: 10.7910/dvn/3dibrd
title: A04_14117.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/e3a64ac9-5596-8ea0-1e3c-8b62d95b930b'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/e3a64ac9-5596-8ea0-1e3c-8b62d95b930b
DOI: 10.7910/dvn/epggsj
title: A04_14117a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/2d72250b-60d7-33a4-cefd-527b5b72c0ed'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/2d72250b-60d7-33a4-cefd-527b5b72c0ed
DOI: 10.15468/dl.aytfyz
title: Occurrence Download

description: A dataset containing 552 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is China",
 "TaxonKey is Triadica sebifera (L.) Small",
 "Year 2013-2024"
 ]
}

 The dataset includes 552 records from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0031863-241007104925546/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.7910/dvn/wwa0j2
title: A04_14118.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/ab317e7c-7e3c-00ef-14c4-75e479a19fc4'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/ab317e7c-7e3c-00ef-14c4-75e479a19fc4
DOI: 10.15468/dl.e6ktr4
title: Occurrence Download

description: A dataset containing 13457 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Phengodidae"
 ]
}

 The dataset includes 13457 records from 106 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0031862-241007104925546/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.7910/dvn/mvgags
title: A04_14118a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/f2fce629-c3ba-b6f7-575e-56412f6435de'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/f2fce629-c3ba-b6f7-575e-56412f6435de
DOI: 10.7910/dvn/8vpzkx
title: A04_14119.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/aabc7e5d-35f6-504d-2cb4-67547c07b711'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/aabc7e5d-35f6-504d-2cb4-67547c07b711
DOI: 10.7910/dvn/bdmy4n
title: A04_14119a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/d47a3683-0af1-0b09-6c4a-4fda145c5adb'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/d47a3683-0af1-0b09-6c4a-4fda145c5adb
DOI: 10.7910/dvn/nz1seu
title: A04_14120a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/c71c4eae-f2a4-236b-b683-a0caae8635fd'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/c71c4eae-f2a4-236b-b683-a0caae8635fd
DOI: 10.7910/dvn/mlqgff
title: A04_14121.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/c1963301-d895-38df-c567-2ca424cf0cfa'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/c1963301-d895-38df-c567-2ca424cf0cfa
DOI: 10.7910/dvn/akv76g
title: A04_14121a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/46ce3a1f-c1b2-f7c7-e553-27de392bcf1e'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/46ce3a1f-c1b2-f7c7-e553-27de392bcf1e
DOI: 10.5281/zenodo.13928297
title: Half-integral polygons with few interior lattice points

description: This record contains



maximal half-integral polygons with up to 40 interior lattice points,

all half-integral polygons with up to 12 interior lattice points,

all Ehrhart quasipolynomials of half-integral polygons with up to 16 interior lattice points,

all half-integral polygons with up to 15 collinear interior lattice points.


The maximal polygons are stored as text files with one polygon per line. Each line contains the vertices of the polygon multiplied by two (so that they are integral). The other polygons as well as the Ehrhart quasipolynomials are stored using the HDF5 file format. All polygons and Ehrhart quasipolynomials have been obtained using RationalPolygons.jl.

Structure of the HDF5 files for polygons

In the HDF5 files "all_i<i>.h5", the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the half-integral polygons with \(8\) interior lattice points having normalized area \(60\) with \(5\) vertices are located in "all_i8.h5" under the dataset "/a60/n5". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon multiplied by two, stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((2\cdot x_1,2\cdot y_1,2 \cdot x_2,2\cdot y_2,2 \cdot x_3,2 \cdot y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.

Structure of the HDF5 files for Ehrhart quasipolynomials

In the HDF5 files "ehrhart_k<k>.h5", the Ehrhart quasipolynomials are split into different datasets according to the normalized area of the associated polygon. We use "a" for the normalized area (twice the euclidian area). For example, the Ehrhart quasipolynomials of all half-integral polygons \(8\) interior lattice points having normalized area \(60\) are located in "ehrhart_i8.h5" under the dataset "/a60". Each Ehrhart quasipolynomial is stored as a \(3 \times 2\) integral matrix. Hence each dataset is three-dimensional, with the first dimension to enumerate the quasipolynomials and the latter two dimensions to store each quasipolynomial itself. For the way Ehrhart quasipolynomials are encoded as \(3 \times 2\) integral matrices, we refer to the relevant documentation of RationalPolygons.jl.
DOI: 10.5281/zenodo.13928298
title: Half-integral polygons with few interior lattice points

description: This record contains



maximal half-integral polygons with up to 40 interior lattice points,

all half-integral polygons with up to 12 interior lattice points,

all Ehrhart quasipolynomials of half-integral polygons with up to 16 interior lattice points,

all half-integral polygons with up to 15 collinear interior lattice points.


The maximal polygons are stored as text files with one polygon per line. Each line contains the vertices of the polygon multiplied by two (so that they are integral). The other polygons as well as the Ehrhart quasipolynomials are stored using the HDF5 file format. All polygons and Ehrhart quasipolynomials have been obtained using RationalPolygons.jl.

Structure of the HDF5 files for polygons

In the HDF5 files "all_i<i>.h5", the polygons are split into different datasets according to their normalized area and number of vertices. We use "a" to denote the normalized area (twice the euclidian area) and "n" to denote the number of vertices. For example, the half-integral polygons with \(8\) interior lattice points having normalized area \(60\) with \(5\) vertices are located in "all_i8.h5" under the dataset "/a60/n5". Each dataset of polygons is one-dimensional with one entry per polygon. A polygon is stored using a compound datatype with \(2 \cdot n\) fields of integers. These integers are the vertices of the polygon multiplied by two, stored in column major layout. For example, a triangle with vertices \((x_1,y_1), (x_2,y_2)\) and \((x_3,y_3)\) is stored as the tuple \((2\cdot x_1,2\cdot y_1,2 \cdot x_2,2\cdot y_2,2 \cdot x_3,2 \cdot y_3)\). Moreover, each file contains the special two-dimensional dataset "numbers_of_polygons" that stores the numbers of polygons for a given normalized volume and number of vertices.

Structure of the HDF5 files for Ehrhart quasipolynomials

In the HDF5 files "ehrhart_k<k>.h5", the Ehrhart quasipolynomials are split into different datasets according to the normalized area of the associated polygon. We use "a" for the normalized area (twice the euclidian area). For example, the Ehrhart quasipolynomials of all half-integral polygons \(8\) interior lattice points having normalized area \(60\) are located in "ehrhart_i8.h5" under the dataset "/a60". Each Ehrhart quasipolynomial is stored as a \(3 \times 2\) integral matrix. Hence each dataset is three-dimensional, with the first dimension to enumerate the quasipolynomials and the latter two dimensions to store each quasipolynomial itself. For the way Ehrhart quasipolynomials are encoded as \(3 \times 2\) integral matrices, we refer to the relevant documentation of RationalPolygons.jl.
DOI: 10.15468/dl.phmzea
title: Occurrence Download

description: A dataset containing 795 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is China",
 "TaxonKey is Triadica sebifera (L.) Small",
 "Year 2000-2024"
 ]
}

 The dataset includes 795 records from 23 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0031864-241007104925546/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.7910/dvn/hrhpus
title: A04_14122.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/c45548c8-0903-bc6f-0c0b-e613424af41f'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/c45548c8-0903-bc6f-0c0b-e613424af41f
DOI: 10.7910/dvn/u0wbhc
title: A04_14122a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/7006cbf2-2eef-61e2-dfd3-a3057eb19519'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/7006cbf2-2eef-61e2-dfd3-a3057eb19519
DOI: 10.7910/dvn/mk7qqf
title: A04_14123.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/dc74e43f-c33e-f0d9-8794-1d0edb4ae28d'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/dc74e43f-c33e-f0d9-8794-1d0edb4ae28d
DOI: 10.7910/dvn/snnecn
title: A04_14124a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/c0f6d130-14ea-c74c-c202-a62186c7dd4f'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/c0f6d130-14ea-c74c-c202-a62186c7dd4f
DOI: 10.7910/dvn/qguhjn
title: A04_14125.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/fbfd3572-50e5-966b-96a1-2f83571804eb'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/fbfd3572-50e5-966b-96a1-2f83571804eb
DOI: 10.7910/dvn/3wener
title: A04_14125a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/c51c0fb7-e07c-0864-028c-72c796f6a3d4'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/c51c0fb7-e07c-0864-028c-72c796f6a3d4
DOI: 10.7910/dvn/olfodt
title: A04_14126a.JPG

description: Link to OCHRE database: &lt;a href = 'http://pi.lib.uchicago.edu/1001/org/ochre/2d493959-537c-a8f2-994b-e35b7a31deab'&gt;http://pi.lib.uchicago.edu/1001/org/ochre/2d493959-537c-a8f2-994b-e35b7a31deab