Ehrhart theory of lattice path matroid polytopes

We study h*-vectors of lattice path matroids polytopes. Since these polytopes are alcoved, as a first step, we provide a combinatorial toolkit for the analysis of such vectors of this larger family. Based on this, we obtain a combinatorial interpretation of the h*-vector of lattice path matroids of...

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Autores:
Valencia Porras, Jerónimo
Tipo de recurso:
Fecha de publicación:
2021
Institución:
Universidad de los Andes
Repositorio:
Séneca: repositorio Uniandes
Idioma:
spa
OAI Identifier:
oai:repositorio.uniandes.edu.co:1992/55092
Acceso en línea:
http://hdl.handle.net/1992/55092
Palabra clave:
Vectores de politopos
Matroides
Caminos reticulares
Politopos
Matemáticas
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-sa/4.0/
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spelling Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Knauer, Kolja26b874f1-7fc5-42f8-81e8-3de35b8f4c4d500Benedetti Velásquez, Carolinavirtual::4996-1Valencia Porras, Jerónimobde33df1-0ce7-455e-9e03-a0a9864ca5b8400Bogart, TristramMorales, Alejandro2022-02-22T19:50:25Z2022-02-22T19:50:25Z2021http://hdl.handle.net/1992/5509225855.pdfinstname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/We study h*-vectors of lattice path matroids polytopes. Since these polytopes are alcoved, as a first step, we provide a combinatorial toolkit for the analysis of such vectors of this larger family. Based on this, we obtain a combinatorial interpretation of the h*-vector of lattice path matroids of rank 2. This yields formulas for the h*-vector and the volume of such matroid polytopes. Furthermore, we characterize Gorenstein lattice path matroids.Este trabajo contiene un estudio de h*-vectores de politopos de matroides de caminos reticulares. Dado que estos politopos son alcobados, como primer paso, se dan herramientas combionatorias para el análisis de tales vectores para esta familia. Basados en esto, se obtienen interpretaciones combinatorias para el h*-vector de politopos de matroides de caminos reticulares de rango 2. Esto da fórmulas para el h*-vector y el volumen de éstas matroides. Además se caracterizan las matroides de caminos reticulares que son Gorenstein.Magíster en MatemáticasMaestría71 páginasapplication/pdfspaUniversidad de los AndesMaestría en MatemáticasFacultad de CienciasDepartamento de MatemáticasEhrhart theory of lattice path matroid polytopesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMVectores de politoposMatroidesCaminos reticularesPolitoposMatemáticas201512556Publication8f535841-abba-4c33-9583-f841a74a4e66virtual::4996-18f535841-abba-4c33-9583-f841a74a4e66virtual::4996-1ORIGINAL25855.pdfapplication/pdf934299https://repositorio.uniandes.edu.co/bitstreams/0d549157-5cad-4528-a27f-4fdd92bf318a/downloadf5f8083765d213f7bbc2242cf69afbf9MD51THUMBNAIL25855.pdf.jpg25855.pdf.jpgIM Thumbnailimage/jpeg5877https://repositorio.uniandes.edu.co/bitstreams/3a2c0f68-1a0b-4e92-b252-278e2aea3472/download1fa552943687a35fe4b78c8a0502e6adMD53TEXT25855.pdf.txt25855.pdf.txtExtracted texttext/plain131707https://repositorio.uniandes.edu.co/bitstreams/f8594bd5-0431-43df-a43a-4622f9809156/downloadf724630e66f44d7d2547f219c667167fMD521992/55092oai:repositorio.uniandes.edu.co:1992/550922024-03-13 12:49:38.024http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.co
dc.title.eng.fl_str_mv Ehrhart theory of lattice path matroid polytopes
title Ehrhart theory of lattice path matroid polytopes
spellingShingle Ehrhart theory of lattice path matroid polytopes
Vectores de politopos
Matroides
Caminos reticulares
Politopos
Matemáticas
title_short Ehrhart theory of lattice path matroid polytopes
title_full Ehrhart theory of lattice path matroid polytopes
title_fullStr Ehrhart theory of lattice path matroid polytopes
title_full_unstemmed Ehrhart theory of lattice path matroid polytopes
title_sort Ehrhart theory of lattice path matroid polytopes
dc.creator.fl_str_mv Valencia Porras, Jerónimo
dc.contributor.advisor.spa.fl_str_mv Knauer, Kolja
dc.contributor.advisor.none.fl_str_mv Benedetti Velásquez, Carolina
dc.contributor.author.spa.fl_str_mv Valencia Porras, Jerónimo
dc.contributor.jury.spa.fl_str_mv Bogart, Tristram
Morales, Alejandro
dc.subject.keyword.none.fl_str_mv Vectores de politopos
Matroides
Caminos reticulares
Politopos
topic Vectores de politopos
Matroides
Caminos reticulares
Politopos
Matemáticas
dc.subject.themes.none.fl_str_mv Matemáticas
description We study h*-vectors of lattice path matroids polytopes. Since these polytopes are alcoved, as a first step, we provide a combinatorial toolkit for the analysis of such vectors of this larger family. Based on this, we obtain a combinatorial interpretation of the h*-vector of lattice path matroids of rank 2. This yields formulas for the h*-vector and the volume of such matroid polytopes. Furthermore, we characterize Gorenstein lattice path matroids.
publishDate 2021
dc.date.issued.none.fl_str_mv 2021
dc.date.accessioned.none.fl_str_mv 2022-02-22T19:50:25Z
dc.date.available.none.fl_str_mv 2022-02-22T19:50:25Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
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status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/1992/55092
dc.identifier.pdf.spa.fl_str_mv 25855.pdf
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url http://hdl.handle.net/1992/55092
identifier_str_mv 25855.pdf
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dc.language.iso.spa.fl_str_mv spa
language spa
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eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv 71 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad de los Andes
dc.publisher.program.spa.fl_str_mv Maestría en Matemáticas
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias
dc.publisher.department.spa.fl_str_mv Departamento de Matemáticas
institution Universidad de los Andes
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