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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/264584
Ver los metadatos del registro completo
id |
CONICETDig_10a6dfa1010db012e05aeebbbc939edd |
---|---|
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 Técnicas2025-09-29T09:52:44Zoai: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:34982025-09-29 09:52:45.022CONICET 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 |
_version_ |
1844613616351838208 |
score |
13.070432 |