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Factorization patterns on nonlinear families of univariate polynomials over a finite field

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dc.contributor.authorMatera, Guillermo
dc.contributor.authorPrivitelli, Melina Lorena
dc.contributor.authorPérez, Mariana Valeria
dc.date.accessioned2025-01-30T15:57:43Z
dc.date.available2025-01-30T15:57:43Z
dc.date.issued2020
dc.description.abstractWe estimate the number |Aλ| of elements on a nonlinear family A of monic polynomials of Fq [T ] of degree r having factorization pattern λ := 1λ1 2λ2 ...rλr . We show that |Aλ| = T (λ) qr−m + O(qr−m−1/2), where T (λ) is the proportion of elements of the symmetric group of r elements with cycle pattern λ and m is the codimension of A. We provide explicit upper bounds for the constants underlying the O-notation in terms of λ and A with “good” behavior. We also apply these results to analyze the average-case complexity of the classical factorization algorithm restricted to A, showing that it behaves as good as in the general case.
dc.description.filiationFil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
dc.description.filiationFil: Pérez, Mariana Valeria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Hurlingham. Instituto de de Tecnologia e Ingenieria.; Argentina
dc.description.filiationFil: Privitelli, Melina Lorena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
dc.format.mimetypeapplication/pdf
dc.identifier.citationMatera, Guillermo; Pérez, Mariana Valeria; Privitelli, Melina Lorena; Factorization patterns on nonlinear families of univariate polynomials over a finite field (2019) Journal Of Algebraic Combinatorics, 51, pp. 103–153
dc.identifier.doihttp://dx.doi.org/10.1007/s10801-018-0869-4
dc.identifier.issn0925-9899
dc.identifier.urihttps://link.springer.com/article/10.1007/s10801-018-0869-4
dc.identifier.urihttps://repositorio.unahur.edu.ar/handle/123456789/529
dc.journal.number51
dc.journal.pagination103-153
dc.journal.titleJournal of Algebraic Combinatorics
dc.language.isoeng
dc.publisherSpringer
dc.rights.licenseinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.subject.ocde1Ciencias Exactas y Naturales
dc.subject.ocde2Matemáticas
dc.subject.unahurCiencias Básicas y Aplicadas
dc.titleFactorization patterns on nonlinear families of univariate polynomials over a finite field
dc.typeinfo:eu-repo/semantics/article
dc.type.oaireinfo:eu-repo/semantics/article
dc.type.snrdinfo:ar-repo/semantics/artículo
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dspace.entity.typePublication
relation.isAuthorOfPublication550d3f91-c6af-4379-a094-54e886b72955
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