@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-00839652v2> a dcat:Dataset ;
    dct:description """
              Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal $I$ in a polynomial ring a monomial ideal ${\\rm in}_\\prec I$, in some special situations the monomial ideal ${\\rm in}_\\prec I$ is square free. On the other hand given any monomial ideal $I$ of a polynomial ring $S$, we can define the toric $K[I]\\subset S$. In this paper we will study toric rings defined by Segre embeddings, we will prove that their $h-$ vectors coincides with the so called Simon Newcomb number's in probabilities and combinatorics. We solve the original question of Simon Newcomb by given a formula for the Simon Newcomb's numbers involving only positive integer numbers.
            """ ;
    dct:identifier "hal-00839652" ;
    dct:issued "2026-05-07T09:08:25.765881"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-07T09:08:25.765887"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Segre embeddings, Hilbert series and Newcomb's problem" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00839652v2/resource/ec5fb283-fc0c-4391-b3f9-9c301db7314a> ;
    dcat:keyword "ams13d40-13d0214m25",
        "betti-numbers",
        "grobner-basis",
        "hilbert-series",
        "infoeu-reposemanticspreprint",
        "mathmath-acmathematics-mathcommutative-algebra-mathac",
        "mathmath-agmathematics-mathalgebraic-geometry-mathag",
        "preprints-working-papers-",
        "segre-ring",
        "simon-newcomb-number" ;
    dcat:landingPage <https://hal.science/hal-00839652> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00839652v2/resource/ec5fb283-fc0c-4391-b3f9-9c301db7314a> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-07T09:08:25.774929"^^xsd:dateTime ;
    dct:modified "2026-05-07T09:08:25.749705"^^xsd:dateTime ;
    dct:title "Segre embeddings, Hilbert series and Newcomb's problem" ;
    dcat:accessURL <https://hal.science/hal-00839652> .

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

<https://hal.science/hal-00839652> a foaf:Document .