A theorem about linear rank inequalities that depend on the characteristic of the finite field
Descripción del Articulo
A linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over finite fields of determined characteristics, an...
| Autor: | |
|---|---|
| Formato: | artículo |
| Fecha de Publicación: | 2022 |
| Institución: | Universidad Nacional de Trujillo |
| Repositorio: | Revistas - Universidad Nacional de Trujillo |
| Lenguaje: | inglés |
| OAI Identifier: | oai:ojs.revistas.unitru.edu.pe:article/4177 |
| Enlace del recurso: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177 |
| Nivel de acceso: | acceso abierto |
| Materia: | Mutually complementary vector spaces Binary matrix Finite field Entropy Linear rank inequality Espacios vectoriales mutuamente complementarios Matriz binaria Cuerpo finito Entropía Desigualdad rango lineal |
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A theorem about linear rank inequalities that depend on the characteristic of the finite fieldUn teorema sobre desigualdades rango lineales que dependen de la caractertística del cuerpo finitoPeña Macias, VictorMutually complementary vector spacesBinary matrixFinite fieldEntropyLinear rank inequalityEspacios vectoriales mutuamente complementariosMatriz binariaCuerpo finitoEntropíaDesigualdad rango linealA linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over finite fields of determined characteristics, and does not in general hold over other characteristics. In this paper, using as guide binary matrices whose ranks depend on the finite field where they are defined, we show a theorem which explicitly produces characteristic-dependent linear rank inequalities; this theorem generalizes results previously obtained in the literature.Una desigualdad rango lineal es una desigualdad lineal que es válida para dimensiones de espacios vectoriales sobre un cuerpo finito. Una desigualdad rango lineal dependiente de la característica es también una desigualdad lineal para dimensiones de espacios vectoriales pero ésta es válida sobre cuerpos finitos de determinada característica, y no es válida en general sobre otras características. En este documento, usando como guía matrices binarias cuyos rangos dependen del cuerpo finito en donde están definidas, nosotros presentamos un teorema que produce explícitamente desigualdades rango lineales dependientes de la característica; ´este teorema generaliza resultados obtenidos previamente en la literatura.National University of Trujillo - Academic Department of Mathematics2022-07-27info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177Selecciones Matemáticas; Vol. 9 No. 01 (2022): January - July; 150 - 160Selecciones Matemáticas; Vol. 9 Núm. 01 (2022): Enero - Julio; 150 - 160Selecciones Matemáticas; v. 9 n. 01 (2022): Janeiro - Julho; 150 - 1602411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUenghttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177/4993Derechos de autor 2022 Selecciones Matemáticashttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/41772022-07-27T15:32:31Z |
| dc.title.none.fl_str_mv |
A theorem about linear rank inequalities that depend on the characteristic of the finite field Un teorema sobre desigualdades rango lineales que dependen de la caractertística del cuerpo finito |
| title |
A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| spellingShingle |
A theorem about linear rank inequalities that depend on the characteristic of the finite field Peña Macias, Victor Mutually complementary vector spaces Binary matrix Finite field Entropy Linear rank inequality Espacios vectoriales mutuamente complementarios Matriz binaria Cuerpo finito Entropía Desigualdad rango lineal |
| title_short |
A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_full |
A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_fullStr |
A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_full_unstemmed |
A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| title_sort |
A theorem about linear rank inequalities that depend on the characteristic of the finite field |
| dc.creator.none.fl_str_mv |
Peña Macias, Victor |
| author |
Peña Macias, Victor |
| author_facet |
Peña Macias, Victor |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Mutually complementary vector spaces Binary matrix Finite field Entropy Linear rank inequality Espacios vectoriales mutuamente complementarios Matriz binaria Cuerpo finito Entropía Desigualdad rango lineal |
| topic |
Mutually complementary vector spaces Binary matrix Finite field Entropy Linear rank inequality Espacios vectoriales mutuamente complementarios Matriz binaria Cuerpo finito Entropía Desigualdad rango lineal |
| description |
A linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over finite fields of determined characteristics, and does not in general hold over other characteristics. In this paper, using as guide binary matrices whose ranks depend on the finite field where they are defined, we show a theorem which explicitly produces characteristic-dependent linear rank inequalities; this theorem generalizes results previously obtained in the literature. |
| publishDate |
2022 |
| dc.date.none.fl_str_mv |
2022-07-27 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177 |
| url |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177 |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177/4993 |
| dc.rights.none.fl_str_mv |
Derechos de autor 2022 Selecciones Matemáticas https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Derechos de autor 2022 Selecciones Matemáticas https://creativecommons.org/licenses/by/4.0 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
| publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
| dc.source.none.fl_str_mv |
Selecciones Matemáticas; Vol. 9 No. 01 (2022): January - July; 150 - 160 Selecciones Matemáticas; Vol. 9 Núm. 01 (2022): Enero - Julio; 150 - 160 Selecciones Matemáticas; v. 9 n. 01 (2022): Janeiro - Julho; 150 - 160 2411-1783 reponame:Revistas - Universidad Nacional de Trujillo instname:Universidad Nacional de Trujillo instacron:UNITRU |
| instname_str |
Universidad Nacional de Trujillo |
| instacron_str |
UNITRU |
| institution |
UNITRU |
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Revistas - Universidad Nacional de Trujillo |
| collection |
Revistas - Universidad Nacional de Trujillo |
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1846521102552006656 |
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13.377223 |
Nota importante:
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
