A new extension of generalized Pascal-type matrix and their representations via Riordan matrix

The algebraic approach based on Pascal matrices is important in many fields of mathematics, ranging from algebraic geometry to optimization, matrix theory and combinatorics. The core of the proposed approach is to introduce a new family of Pascal-type matrices Ψi,j,c,a[x,y],x,y∈R-{0} with parameters...

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Autores:
Ramírez, William
Urieles, Alejandro
Riyasat, Mumtaz
Ortega Wilches, María José
Siado, Luis
Tipo de recurso:
Article of investigation
Fecha de publicación:
2024
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/14130
Acceso en línea:
https://hdl.handle.net/11323/14130
https://repositorio.cuc.edu.co/
Palabra clave:
Factorization formula
Generalized Pascal matrices
Pell and Fibonacci matrices
Pascal matrices
Riordan matrices
Rights
openAccess
License
Atribución 4.0 Internacional (CC BY 4.0)
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network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.eng.fl_str_mv A new extension of generalized Pascal-type matrix and their representations via Riordan matrix
title A new extension of generalized Pascal-type matrix and their representations via Riordan matrix
spellingShingle A new extension of generalized Pascal-type matrix and their representations via Riordan matrix
Factorization formula
Generalized Pascal matrices
Pell and Fibonacci matrices
Pascal matrices
Riordan matrices
title_short A new extension of generalized Pascal-type matrix and their representations via Riordan matrix
title_full A new extension of generalized Pascal-type matrix and their representations via Riordan matrix
title_fullStr A new extension of generalized Pascal-type matrix and their representations via Riordan matrix
title_full_unstemmed A new extension of generalized Pascal-type matrix and their representations via Riordan matrix
title_sort A new extension of generalized Pascal-type matrix and their representations via Riordan matrix
dc.creator.fl_str_mv Ramírez, William
Urieles, Alejandro
Riyasat, Mumtaz
Ortega Wilches, María José
Siado, Luis
dc.contributor.author.none.fl_str_mv Ramírez, William
Urieles, Alejandro
Riyasat, Mumtaz
Ortega Wilches, María José
Siado, Luis
dc.subject.proposal.eng.fl_str_mv Factorization formula
Generalized Pascal matrices
Pell and Fibonacci matrices
Pascal matrices
Riordan matrices
topic Factorization formula
Generalized Pascal matrices
Pell and Fibonacci matrices
Pascal matrices
Riordan matrices
description The algebraic approach based on Pascal matrices is important in many fields of mathematics, ranging from algebraic geometry to optimization, matrix theory and combinatorics. The core of the proposed approach is to introduce a new family of Pascal-type matrices Ψi,j,c,a[x,y],x,y∈R-{0} with parameters c,a∈R+-{1}. By employing the effective matrix algebra tools, certain algebraic properties including the product formula, inverse matrix, determinant and eigen values are determined for the Pascal matrix Ψi,j,c,a[x,y]. Further, some new families of matrices like the Fibonacci Fi,j,c,a[x,y], Lucas Li,j,c,a[x,y], Pell Si,j,c,a[x,y] and other matrices are introduced and these are employed to derive factorization formulae for the Pascal matrix Ψi,j,c,a[x,y] involving Riordan matrix. Finally, the properties and representations derived above for these matrices are further demonstrated for a matrix of particular order 3.
publishDate 2024
dc.date.issued.none.fl_str_mv 2024-04-12
dc.date.accessioned.none.fl_str_mv 2025-04-11T15:02:37Z
dc.date.available.none.fl_str_mv 2025-04-11T15:02:37Z
dc.type.none.fl_str_mv Artículo de revista
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dc.type.content.none.fl_str_mv Text
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dc.identifier.citation.none.fl_str_mv Ramírez, W., Urieles, A., Riyasat, M. et al. A new extension of generalized Pascal-type matrix and their representations via Riordan matrix. Bol. Soc. Mat. Mex. 30, 41 (2024). https://doi.org/10.1007/s40590-024-00609-4
dc.identifier.issn.none.fl_str_mv 1405-213X
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/11323/14130
dc.identifier.doi.none.fl_str_mv 10.1007/s40590-024-00609-4
dc.identifier.eissn.none.fl_str_mv 2296-4495
dc.identifier.instname.none.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.none.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.none.fl_str_mv https://repositorio.cuc.edu.co/
identifier_str_mv Ramírez, W., Urieles, A., Riyasat, M. et al. A new extension of generalized Pascal-type matrix and their representations via Riordan matrix. Bol. Soc. Mat. Mex. 30, 41 (2024). https://doi.org/10.1007/s40590-024-00609-4
1405-213X
10.1007/s40590-024-00609-4
2296-4495
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/14130
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.ispartofjournal.none.fl_str_mv Boletin de la Sociedad Matematica Mexicana
dc.relation.references.none.fl_str_mv Brawer, R., Pirovino, M. The linear algebra of the Pascal matrix (1992) Linear Algebra Appl, 174, pp. 13-23. 1176447
Call, G.S., Velleman, D.J. Pascal’s matrices (1993) Amer. Math. Monthly, 100, pp. 372-376. 1209465
Gwang, Y., Seon, C. The generalized Pascal matrix via the generalized Fibonacci matrix and the generalized Pell matrix (2008) J. Korean Math. Soc, 45, pp. 479-491. 2389550
Jeelani, M.B. On employing linear algebra approach to hybrid Sheffer polynomials (2023) AIMS Mathematics, 8 (1), pp. 1871-1888. 4501160
Khan, S., Nahid, T. Certain properties of the Laguerre-Sheffer polynomials (2022) J. Anal, 30, pp. 245-269. 4390613
Lee, G.-Y., Kim, J.-S., Lee, S.-G. Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices (2002) Fibonacci Quart, 40 (3), pp. 203-211. 1913345
Nahid, T., Alam, P., Choi, J. Matrix approaches for Gould-Hopper-Laguerre-Sheffer matrix polynomial identities (2023) Axioms, 12 (7), p. 621.
Peart, P., Woodson, L. Triple factorization of some Riordan matrices (1993) Fibonacci Quart, 31 (2), pp. 121-128. 1214678
Quintana, Y., Ramírez, W., Urieles, A. Generalized Apostol-type polynomial matrix and its algebraic properties (2019) Math. Rep, 21 (71), pp. 249-264. 3976960
Quintana, Y., Ramírez, W., Urieles, A. Euler matrices and their algebraic properties revisited (2020) Appl. Math. Inf. Sci, 14, pp. 1-14. 4057245
Riyasat, M. A Riordan array approach to Apostol type-Sheffer sequences (2019) Filomat, 33 (18), pp. 6025-6038. 4054402
Riyasat, M., Haneef, M., Khan, S. Some properties of degenerate Sheffer sequences based on algebraic approach (2023) Indian J. Pure Appl. Math,
Shapiro, L.W., Getu, S., Woan, W.J., Woodson, L.C. The Riordan group (1991) Discrete Appl. Math, 34, pp. 229-239. 1137996
Srivastava, H.M., Riyasat, M., Khan, S., Araci, S., Acikgoz, M. A new approach to Legendre-truncated-exponential based Sheffer sequences via Riordan arrays (2020) Appl. Math. Comput, 369. 4038193
Stanimirović, P., Nikolov, J., Stanimirović, I. A generalization of Fibonacci and Lucas matrices (2008) Discrete Appl. Math, 156 (14), pp. 2606-2619. 2451084
Wani, S.A., Nahid, T., Hussain, K., Jeelani, M.B. A unified matrix approach to the Legendre-Sheffer and certain hybrid polynomial sequences (2023) J. Anal.,
Zhang, Z.Z. The linear algebra of generalized Pascal matrix (1997) Linear Algebra Appl, 250, pp. 51-60. 1420570
Zhang, Z.Z., Liu, M.X. An extension of generalized Pascal matrix and its algebraic properties (1998) Linear Algebra Appl, 271, pp. 169-177. 1485166
Zhang, Z., Zhang, Y. The Lucas matrix and some combinatorial identities (2007) Indian J. Pure Appl. Math, 38 (5), pp. 457-465. 2361599
dc.relation.citationissue.none.fl_str_mv 41
dc.relation.citationvolume.none.fl_str_mv 30
dc.rights.eng.fl_str_mv © The Author(s) 2024.
dc.rights.license.none.fl_str_mv Atribución 4.0 Internacional (CC BY 4.0)
dc.rights.uri.none.fl_str_mv https://creativecommons.org/licenses/by/4.0/
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rights_invalid_str_mv Atribución 4.0 Internacional (CC BY 4.0)
© The Author(s) 2024.
https://creativecommons.org/licenses/by/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Birkhauser Verlag Basel
dc.publisher.place.none.fl_str_mv Switzerland
publisher.none.fl_str_mv Birkhauser Verlag Basel
dc.source.none.fl_str_mv https://link.springer.com/article/10.1007/s40590-024-00609-4
institution Corporación Universidad de la Costa
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spelling Atribución 4.0 Internacional (CC BY 4.0)© The Author(s) 2024.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Ramírez, Williamvirtual::1108-1Urieles, AlejandroRiyasat, MumtazOrtega Wilches, María Josévirtual::1109-1Siado, Luis2025-04-11T15:02:37Z2025-04-11T15:02:37Z2024-04-12Ramírez, W., Urieles, A., Riyasat, M. et al. A new extension of generalized Pascal-type matrix and their representations via Riordan matrix. Bol. Soc. Mat. Mex. 30, 41 (2024). https://doi.org/10.1007/s40590-024-00609-41405-213Xhttps://hdl.handle.net/11323/1413010.1007/s40590-024-00609-42296-4495Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/The algebraic approach based on Pascal matrices is important in many fields of mathematics, ranging from algebraic geometry to optimization, matrix theory and combinatorics. The core of the proposed approach is to introduce a new family of Pascal-type matrices Ψi,j,c,a[x,y],x,y∈R-{0} with parameters c,a∈R+-{1}. By employing the effective matrix algebra tools, certain algebraic properties including the product formula, inverse matrix, determinant and eigen values are determined for the Pascal matrix Ψi,j,c,a[x,y]. Further, some new families of matrices like the Fibonacci Fi,j,c,a[x,y], Lucas Li,j,c,a[x,y], Pell Si,j,c,a[x,y] and other matrices are introduced and these are employed to derive factorization formulae for the Pascal matrix Ψi,j,c,a[x,y] involving Riordan matrix. Finally, the properties and representations derived above for these matrices are further demonstrated for a matrix of particular order 3.application/pdfengBirkhauser Verlag BaselSwitzerlandhttps://link.springer.com/article/10.1007/s40590-024-00609-4A new extension of generalized Pascal-type matrix and their representations via Riordan matrixArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Boletin de la Sociedad Matematica MexicanaBrawer, R., Pirovino, M. The linear algebra of the Pascal matrix (1992) Linear Algebra Appl, 174, pp. 13-23. 1176447Call, G.S., Velleman, D.J. Pascal’s matrices (1993) Amer. Math. Monthly, 100, pp. 372-376. 1209465Gwang, Y., Seon, C. The generalized Pascal matrix via the generalized Fibonacci matrix and the generalized Pell matrix (2008) J. Korean Math. Soc, 45, pp. 479-491. 2389550Jeelani, M.B. On employing linear algebra approach to hybrid Sheffer polynomials (2023) AIMS Mathematics, 8 (1), pp. 1871-1888. 4501160Khan, S., Nahid, T. Certain properties of the Laguerre-Sheffer polynomials (2022) J. Anal, 30, pp. 245-269. 4390613Lee, G.-Y., Kim, J.-S., Lee, S.-G. Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices (2002) Fibonacci Quart, 40 (3), pp. 203-211. 1913345Nahid, T., Alam, P., Choi, J. Matrix approaches for Gould-Hopper-Laguerre-Sheffer matrix polynomial identities (2023) Axioms, 12 (7), p. 621.Peart, P., Woodson, L. Triple factorization of some Riordan matrices (1993) Fibonacci Quart, 31 (2), pp. 121-128. 1214678Quintana, Y., Ramírez, W., Urieles, A. Generalized Apostol-type polynomial matrix and its algebraic properties (2019) Math. Rep, 21 (71), pp. 249-264. 3976960Quintana, Y., Ramírez, W., Urieles, A. Euler matrices and their algebraic properties revisited (2020) Appl. Math. Inf. Sci, 14, pp. 1-14. 4057245Riyasat, M. A Riordan array approach to Apostol type-Sheffer sequences (2019) Filomat, 33 (18), pp. 6025-6038. 4054402Riyasat, M., Haneef, M., Khan, S. Some properties of degenerate Sheffer sequences based on algebraic approach (2023) Indian J. Pure Appl. Math,Shapiro, L.W., Getu, S., Woan, W.J., Woodson, L.C. The Riordan group (1991) Discrete Appl. Math, 34, pp. 229-239. 1137996Srivastava, H.M., Riyasat, M., Khan, S., Araci, S., Acikgoz, M. A new approach to Legendre-truncated-exponential based Sheffer sequences via Riordan arrays (2020) Appl. Math. Comput, 369. 4038193Stanimirović, P., Nikolov, J., Stanimirović, I. A generalization of Fibonacci and Lucas matrices (2008) Discrete Appl. Math, 156 (14), pp. 2606-2619. 2451084Wani, S.A., Nahid, T., Hussain, K., Jeelani, M.B. A unified matrix approach to the Legendre-Sheffer and certain hybrid polynomial sequences (2023) J. Anal.,Zhang, Z.Z. The linear algebra of generalized Pascal matrix (1997) Linear Algebra Appl, 250, pp. 51-60. 1420570Zhang, Z.Z., Liu, M.X. An extension of generalized Pascal matrix and its algebraic properties (1998) Linear Algebra Appl, 271, pp. 169-177. 1485166Zhang, Z., Zhang, Y. The Lucas matrix and some combinatorial identities (2007) Indian J. Pure Appl. Math, 38 (5), pp. 457-465. 23615994130Factorization formulaGeneralized Pascal matricesPell and Fibonacci matricesPascal matricesRiordan matricesPublication38aeab65-0e76-44a5-8e3e-a13f48515f3dvirtual::1108-1a817bb11-dc35-4174-8eb8-66c8d1c67dbfvirtual::1109-138aeab65-0e76-44a5-8e3e-a13f48515f3dvirtual::1108-1a817bb11-dc35-4174-8eb8-66c8d1c67dbfvirtual::1109-10000-0003-4675-0221virtual::1108-10000-0002-4563-6286virtual::1109-1ORIGINALA new extension of generalized Pascal-type matrix and their representations via Riordan matrix.pdfA new extension of generalized Pascal-type matrix and their representations via Riordan matrix.pdfapplication/pdf154044https://repositorio.cuc.edu.co/bitstreams/629ad416-9a7b-47cb-bb1f-ba5ecec46e63/downloada57298e1432f8068e4a453a0402cc2e9MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-815543https://repositorio.cuc.edu.co/bitstreams/b5c11271-e343-49a0-96d0-ccffc4af3d3d/download73a5432e0b76442b22b026844140d683MD52TEXTA new extension of generalized 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ara ejercer estos derechos sobre la Obra tal y como se indica a continuación:</p>
    <ol type="a">
      <li>Reproducir la Obra, incorporar la Obra en una o más Obras Colectivas, y reproducir la Obra incorporada en las Obras Colectivas.</li>
      <li>Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.</li>
      <li>Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.</li>
    </ol>
    <p>Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).</p>
  </li>
  <br/>
  <li>
    Restricciones.
    <p>La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:</p>
    <ol type="a">
      <li>Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).</li>
      <li>Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.</li>
      <li>Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.</li>
      <li>
        Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:
        <ol type="i">
          <li>Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.</li>
          <li>Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.</li>
        </ol>
      </li>
      <li>Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.</li>
    </ol>
  </li>
  <br/>
  <li>
    Representaciones, Garantías y Limitaciones de Responsabilidad.
    <p>A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.</p>
  </li>
  <br/>
  <li>
    Limitación de responsabilidad.
    <p>A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.</p>
  </li>
  <br/>
  <li>
    Término.
    <ol type="a">
      <li>Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.</li>
      <li>Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.</li>
    </ol>
  </li>
  <br/>
  <li>
    Varios.
    <ol type="a">
      <li>Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.</li>
      <li>Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.</li>
      <li>Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.</li>
      <li>Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.</li>
    </ol>
  </li>
  <br/>
</ol>


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