@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-00954973v1> a dcat:Dataset ;
    dct:description """
              Given a b-multiplicative sequence and a prime p, studying the p-rarefaction consists in characterizing the asymptotic behaviour of the sums of the first terms indexed by the multiples of $p$. Under the "finiteness" assumption for the sequence, the integer values of the homogeneous "norm" 3-variate polynomial $\\mathcal N_{p,i_1,i_2}(Y_0,Y_1,Y_2):=\\prod_{j=1}^{p-1} (Y_0+\\zeta_p^{i_1j}Y_1+\\zeta_p^{i_2j}Y_2),$ where $i_1,i_2\\in\\{1,2,...,p-1\\},$ and $\\zeta_p$ is a primitive p-th root of unity, determine this asymptotic behaviour. It will be shown that a combinatorial method can be applied to $\\mathcal N_{p,i_1,i_2}(Y_0,Y_1,Y_2).$ The method enables deducing functional relations between the coefficients as well as various properties of the coefficients of $\\mathcal N_{p,i_1,i_2}(Y_0,Y_1,Y_2)$, in particular for $i_1=1, i_2=2,3.$ This method provides relations between binomial coefficients. It gives new proofs of the two identities $\\prod_{j=1}^{p-1} (1-\\zeta_p^j\\right)=p$ and $\\prod_{j=1}^{p-1} (1+\\zeta_p^j-\\zeta_p^{2j})=L_p$ (the p-th Lucas number). The sign and the residue modulo $p$ of the symmetric polynomials of $1+\\zeta-\\zeta_p^2$ can also be obtained. An algorithm for computation of coefficients of $\\mathcal N_{p,i_1,i_2}(Y_0,Y_1,Y_2)$ is developed.
            """ ;
    dct:identifier "hal-00954973" ;
    dct:issued "2026-05-06T03:56:57.508171"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-06T03:56:57.508175"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "A combinatorial approach to rarefaction in b-multiplicative sequences." ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00954973v1/resource/380813f0-d007-4ff2-84ea-515ee799bfb0> ;
    dcat:keyword "05-a-10-05-a-18-11-b-39-11-r-18",
        "b-multiplicative-sequences",
        "binomial-coefficients",
        "cyclotomic-extensions",
        "infoeu-reposemanticspreprint",
        "mathmath-ntmathematics-mathnumber-theory-mathnt",
        "preprints-working-papers-",
        "rarefaction",
        "set-partitions" ;
    dcat:landingPage <https://hal.science/hal-00954973> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00954973v1/resource/380813f0-d007-4ff2-84ea-515ee799bfb0> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-06T03:56:57.534211"^^xsd:dateTime ;
    dct:modified "2026-05-06T03:56:57.493628"^^xsd:dateTime ;
    dct:title "A combinatorial approach to rarefaction in b-multiplicative sequences." ;
    dcat:accessURL <https://hal.science/hal-00954973> .

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