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DC Field | Value | Language |
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dc.contributor.author | Peña Macias, Victor | - |
dc.contributor.author | Sarria Zapata, Humberto | - |
dc.date.accessioned | 2021-12-10T00:08:44Z | - |
dc.date.available | 2021-12-10T00:08:44Z | - |
dc.date.issued | 2019-12-20 | - |
dc.identifier.uri | https://repositorio.accefyn.org.co/handle/001/1179 | - |
dc.description.abstract | En Álgebra Lineal sobre cuerpos finitos, una desigualdad rango lineal dependiente de la característica es una desigualdad lineal que es válida para dimensiones de sumas de subspacios vectoriales de un espacio vectorial de dimensión finita sobre un cuerpo finito de determinada característica, y no es válida en general sobre cualquier cuerpo de otra característica. Este documento presenta un resultado preliminar referente a la producción de estas desigualdades. Nosotros producimos tres desigualdades nuevas en 21 variables usando como guía una matriz binaria particular, con entradas en un cuerpo finito, cuyo rango es 8, 9 o 10 dependiendo de que la característica sea 2, 3 o distinta de 2 y 3; la primera desigualdad es válida sobre cuerpos de característica 2; la segunda es válida sobre cuerpos de característica 2 o 3; la tercera es válida sobre cuerpos de característica distinta de 2 y 3. | spa |
dc.description.abstract | In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of spans of vector subspaces of a finite dimensional vector space over a finite field of determined characteristic, and does not in general hold over fields with other characteristic. This paper shows a preliminary result in the production of these inequalities. We produce three new inequalities in 21 variables using as guide a particular binary matrix, with entries in a finite field, whose rank is 8, with characteristic 2; 9 with characteristic 3; or 10 with characteristic neither 2 nor 3. The first inequality is true over fields whose characteristic is 2; the second inequality is true over fields whose characteristic is 2 or 3; the third inequality is true over fields whose characteristic is neither 2 nor 3. | eng |
dc.format.mimetype | application/pdf | spa |
dc.language.iso | spa | spa |
dc.publisher | Academia Colombiana de Ciencias Exactas, Físicas y Naturales | spa |
dc.rights | Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International | spa |
dc.rights.uri | https://creativecommons.org/licenses/by-nc/4.0/ | spa |
dc.source | Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales | spa |
dc.title | Characteristic-dependent linear rank inequalities in 21 variables | spa |
dc.type | Artículo de revista | spa |
dcterms.audience | Estudiantes, Profesores, Comunidad científica colombiana | spa |
dcterms.references | Blasiak A., Kleinberg R., Lubetzky E. (2011). Lexicographic products and the power of non-Linear Network Coding. Foundations of Computer Science (FOCS) 2011 IEEE 52nd Annual Symposium on. 609-618. | spa |
dcterms.references | Dougherty R., Freiling C., Zeger K. (2005). Insufficiency of linear coding in network information flow. IEEE Transactions on Information Theory. 51 (8): 2745-2759. | spa |
dcterms.references | Dougherty R., Freiling C., Zeger K. (2013). Achievable rate regions for Network Coding. IEEE Transactions on Information Theory. 61 (5): 2488-2509. | spa |
dcterms.references | Freiling E.F. (2014). Characteristic dependent linear rank inequalities and applications to Network Coding. Ph.D. thesis. San Diego, The United States: University of California. | spa |
dcterms.references | Ingleton W. (1969). Representation of matroids. Combinatorial mathematics and its applications. Oxford. 149-167. | spa |
dcterms.references | Kinser R. (2011). New inequalities for subspace arrangements. Journal Combinatorial Theory Serie A. 118 (1): 152-161. | spa |
dcterms.references | Shen A., Hammer D., Romashchenko A.E., Vereshchagin N.K. (2000). Inequalities for Shannon entropy and Kolmogorov complexity. Journal of Computer and Systems Sciences. 60: 442-464. | spa |
dc.rights.accessrights | info:eu-repo/semantics/openAccess | spa |
dc.type.driver | info:eu-repo/semantics/article | spa |
dc.type.version | info:eu-repo/semantics/publishedVersion | spa |
dc.rights.creativecommons | Atribución-NoComercial 4.0 Internacional (CC BY-NC 4.0) | spa |
dc.identifier.doi | https://doi.org/10.18257/raccefyn.928 | - |
dc.subject.proposal | Entropía | spa |
dc.subject.proposal | Entropy | eng |
dc.subject.proposal | Desigualdad rango lineal | spa |
dc.subject.proposal | Linear rank inequality | eng |
dc.subject.proposal | Matríz binaria | spa |
dc.subject.proposal | Binary matrix | eng |
dc.subject.proposal | Suma directa de espacios vectoriales | spa |
dc.subject.proposal | Direct sum in vector spaces | eng |
dc.type.coar | http://purl.org/coar/resource_type/c_6501 | spa |
dc.relation.ispartofjournal | Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales | spa |
dc.relation.citationvolume | 43 | spa |
dc.relation.citationstartpage | 764 | spa |
dc.relation.citationendpage | 770 | spa |
dc.publisher.place | Bogotá, Colombia | spa |
dc.contributor.corporatename | Academia Colombiana de Ciencias Exactas, Físicas y Naturales | spa |
dc.relation.citationissue | 169 | spa |
dc.type.content | DataPaper | spa |
dc.type.redcol | http://purl.org/redcol/resource_type/ART | spa |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 | spa |
oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | spa |
Appears in Collections: | BA. Revista de la Academia Colombiana de Ciencias Exactas Físicas y Naturales |
Files in This Item:
File | Description | Size | Format | |
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15. Characteristic-Dependent Linear Rank Inequalitie.pdf | Matemáticas | 242.91 kB | Adobe PDF | View/Open |
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