@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#> .

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    dct:description """
              Ha Minh Lam et M. Morales introduced a family of binomial ideals that are binomial extensions of square free monomial ideals. Let I be a square free monomial ideal of k[x] and J a sum of scroll ideals in k[z] with some extra conditions, we define the binomial extension of I as B=I+J⊂k[z]. The aim of this thesis is to study the biggest number p such that the syzygies of B are linear until the step p-1. Due to some order conditions given to the facets of the Stanley-Reisner complex of I we get an order ≻ for the variables of the polynomial ring k[z]. By a calculation of the Gröbner basis of the ideal B we obtain that the initial ideal in(B) is a square free monomial ideal. We will prove that B is 2-regular iff I is 2-regular. In the general case, wheter I is not 2-regular we will find a lower bound for the the maximal integer q which satisfies that the first q-1 sizygies of B are linear. On the other hand, wheter J is toric and supposing other conditions, we will find a upper bound for the integer q which satisfies that the first q-1 syzygies of B are linear. By given more conditions we will prove that the twobounds are equal.
            """ ;
    dct:identifier "NNT: 2012GRENM043" ;
    dct:issued "2026-05-15T09:54:01.542531"^^xsd:dateTime ;
    dct:language "fr" ;
    dct:modified "2026-05-15T09:54:01.542537"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Betti numbers of binomial ideals" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00772901v1/resource/8d97f3c9-cac2-4fd8-ba4c-e47bfa8f60b1> ;
    dcat:keyword "bases-de-grobner",
        "betti-numbers",
        "clique-complex",
        "complexe-de-cliques",
        "grobner-basis",
        "ideaux-monomiaux",
        "ideaux-toriques",
        "infoeu-reposemanticsdoctoralthesis",
        "mathmath-gmmathematics-mathgeneral-mathematics-mathgm",
        "monomial-ideals",
        "n2p-property",
        "nombre-de-betti",
        "propriete-n2p",
        "theses",
        "torique-ideals" ;
    dcat:landingPage <https://theses.hal.science/tel-00772901> .

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    dct:issued "2026-05-15T09:54:01.621513"^^xsd:dateTime ;
    dct:modified "2026-05-15T09:54:01.512198"^^xsd:dateTime ;
    dct:title "Betti numbers of binomial ideals" ;
    dcat:accessURL <https://theses.hal.science/tel-00772901> .

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