@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00943550v2> a dcat:Dataset ;
    dct:description """
              Given $d+1$ sets of points, or colours, $\\S_1,\\ldots,\\S_{d+1}$ in $\\R^d$, a {\\em colourful simplex} is a set $T\\subseteq\\bigcup_{i=1}^{d+1}\\S_i$ such that $|T\\cap \\S_i|\\leq 1$, for $i=1,\\ldots,d+1$. The colourful \\cara{} theorem states that, if $\\zero$ is in the convex hull of each $\\S_i$, then there exists a colourful simplex $T$ containing $\\zero$ in its convex hull. In 2006, Deza, Huang, Stephen, and Terlaky ({\\em Colourful simplicial depth}, Discrete Comput. Geom., {\\bf 35}, 597--604 (2006)) conjectured that, actually, when $|\\S_i|=d+1$ for all $i=1,\\ldots,d+1$, there are always at least $d^2+1$ colourful simplices containing $\\zero$ in their convex hulls. We prove this conjecture with the help of combinatorial objects called octahedral systems.
            """ ;
    dct:identifier "hal-00943550" ;
    dct:issued "2026-05-06T03:36:47.818437"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-06T03:36:47.818441"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "The colourful simplicial depth conjecture" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00943550v2/resource/efd8e7c5-a153-4ce7-a18d-cfce056deee1> ;
    dcat:keyword "colourful-caratheodory-theorem",
        "colourful-simplicial-depth",
        "infoeu-reposemanticspreprint",
        "infoinfo-dmcomputer-science-csdiscrete-mathematics-csdm",
        "octahedral-systems",
        "preprints-working-papers-" ;
    dcat:landingPage <https://hal.science/hal-00943550> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00943550v2/resource/efd8e7c5-a153-4ce7-a18d-cfce056deee1> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-06T03:36:47.831689"^^xsd:dateTime ;
    dct:modified "2026-05-06T03:36:47.807798"^^xsd:dateTime ;
    dct:title "The colourful simplicial depth conjecture" ;
    dcat:accessURL <https://hal.science/hal-00943550> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://hal.science/hal-00943550> a foaf:Document .