Smooth symmetric systems over a finite field and applications

Autores
Giménez, Nardo; Matera, Guillermo; Pérez, Mariana Valeria; Privitelli, Melina Lorena
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the set of common Fq–rational solutions of “smooth” systems of multivariate symmetric polynomials with coeffi-cients in a finite field Fq. We show that, under certain condi-tions, the set of common solutions of such polynomial systems over the algebraic closure of Fqhas a “good” geometric be-havior. This allows us to obtain precise estimates on the corresponding number of common Fq–rational solutions. In the case of hypersurfaces we are able to strengthen the results. We illustrate the interest of these estimates through their application to certain classical combinatorial problems over finite fields.
Fil: Giménez, Nardo. Universidad Nacional de Hurlingham.; Argentina
Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Pérez, Mariana Valeria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Hurlingham.; Argentina
Fil: Privitelli, Melina Lorena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Hurlingham.; Argentina
Materia
Finite fields
Symmetric polynomials
Complete intersections
Singular locus
Factorization patterns
Deep holes
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/264584
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/264584
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Smooth symmetric systems over a finite field and applicationsGiménez, NardoMatera, GuillermoPérez, Mariana ValeriaPrivitelli, Melina LorenaFinite fieldsSymmetric polynomialsComplete intersectionsSingular locusFactorization patternsDeep holeshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the set of common Fq–rational solutions of “smooth” systems of multivariate symmetric polynomials with coeffi-cients in a finite field Fq. We show that, under certain condi-tions, the set of common solutions of such polynomial systems over the algebraic closure of Fqhas a “good” geometric be-havior. This allows us to obtain precise estimates on the corresponding number of common Fq–rational solutions. In the case of hypersurfaces we are able to strengthen the results. We illustrate the interest of these estimates through their application to certain classical combinatorial problems over finite fields.Fil: Giménez, Nardo. Universidad Nacional de Hurlingham.; ArgentinaFil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Pérez, Mariana Valeria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Hurlingham.; ArgentinaFil: Privitelli, Melina Lorena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Hurlingham.; ArgentinaAcademic Press Inc Elsevier Science2025-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/264584Giménez, Nardo; Matera, Guillermo; Pérez, Mariana Valeria; Privitelli, Melina Lorena; Smooth symmetric systems over a finite field and applications; Academic Press Inc Elsevier Science; Journal of Algebra; 664; 2-2025; 362-4130021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0021869324005180info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2024.09.011info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2312.09477info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:22:09Zoai:ri.conicet.gov.ar:11336/264584instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:22:09.602CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Smooth symmetric systems over a finite field and applications
title Smooth symmetric systems over a finite field and applications
spellingShingle Smooth symmetric systems over a finite field and applications
Giménez, Nardo
Finite fields
Symmetric polynomials
Complete intersections
Singular locus
Factorization patterns
Deep holes
title_short Smooth symmetric systems over a finite field and applications
title_full Smooth symmetric systems over a finite field and applications
title_fullStr Smooth symmetric systems over a finite field and applications
title_full_unstemmed Smooth symmetric systems over a finite field and applications
title_sort Smooth symmetric systems over a finite field and applications
dc.creator.none.fl_str_mv Giménez, Nardo
Matera, Guillermo
Pérez, Mariana Valeria
Privitelli, Melina Lorena
author Giménez, Nardo
author_facet Giménez, Nardo
Matera, Guillermo
Pérez, Mariana Valeria
Privitelli, Melina Lorena
author_role author
author2 Matera, Guillermo
Pérez, Mariana Valeria
Privitelli, Melina Lorena
author2_role author
author
author
dc.subject.none.fl_str_mv Finite fields
Symmetric polynomials
Complete intersections
Singular locus
Factorization patterns
Deep holes
topic Finite fields
Symmetric polynomials
Complete intersections
Singular locus
Factorization patterns
Deep holes
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the set of common Fq–rational solutions of “smooth” systems of multivariate symmetric polynomials with coeffi-cients in a finite field Fq. We show that, under certain condi-tions, the set of common solutions of such polynomial systems over the algebraic closure of Fqhas a “good” geometric be-havior. This allows us to obtain precise estimates on the corresponding number of common Fq–rational solutions. In the case of hypersurfaces we are able to strengthen the results. We illustrate the interest of these estimates through their application to certain classical combinatorial problems over finite fields.
Fil: Giménez, Nardo. Universidad Nacional de Hurlingham.; Argentina
Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Pérez, Mariana Valeria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Hurlingham.; Argentina
Fil: Privitelli, Melina Lorena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Hurlingham.; Argentina
description We study the set of common Fq–rational solutions of “smooth” systems of multivariate symmetric polynomials with coeffi-cients in a finite field Fq. We show that, under certain condi-tions, the set of common solutions of such polynomial systems over the algebraic closure of Fqhas a “good” geometric be-havior. This allows us to obtain precise estimates on the corresponding number of common Fq–rational solutions. In the case of hypersurfaces we are able to strengthen the results. We illustrate the interest of these estimates through their application to certain classical combinatorial problems over finite fields.
publishDate 2025
dc.date.none.fl_str_mv 2025-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/264584
Giménez, Nardo; Matera, Guillermo; Pérez, Mariana Valeria; Privitelli, Melina Lorena; Smooth symmetric systems over a finite field and applications; Academic Press Inc Elsevier Science; Journal of Algebra; 664; 2-2025; 362-413
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/264584
identifier_str_mv Giménez, Nardo; Matera, Guillermo; Pérez, Mariana Valeria; Privitelli, Melina Lorena; Smooth symmetric systems over a finite field and applications; Academic Press Inc Elsevier Science; Journal of Algebra; 664; 2-2025; 362-413
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0021869324005180
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2024.09.011
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2312.09477
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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