On the proof of the upper bound theorem

Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2017, Director: Santiago Zarzuela

Detalles Bibliográficos
Autor: Dediu, Catalin
Tipo de recurso: tesis de maestría
Fecha de publicación:2017
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/121133
Acceso en línea:https://hdl.handle.net/2445/121133
Access Level:acceso abierto
Palabra clave:Àlgebra commutativa
Anells commutatius
Treballs de fi de màster
Geometria combinatòria
Commutative algebra
Commutative rings
Master's theses
Combinatorial geometry
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spelling On the proof of the upper bound theoremDediu, CatalinÀlgebra commutativaAnells commutatiusTreballs de fi de màsterGeometria combinatòriaCommutative algebraCommutative ringsMaster's thesesCombinatorial geometryTreballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2017, Director: Santiago Zarzuela[en] Let $\Delta$ be a triangulation of a $(d - 1)$-dimensional sphere with $n$ vertices. The Upper Bound Conjecture (UBC for short) gives an explicit bound of the number of $i$-dimensional faces of $\Delta$. This question dates back to the beginning of the 1950’s, when the study of the efficiency of some linear programming techniques led to the following problem: Determine the maximal possible number of $i$-faces of d-polytope with $n$ vertices. The first statement of the UBC was formulated in 1957 by Theodore Motzkin. The original result state that the number of $i$-dimensional faces of a $d$-dimensional polytope with n vertices are bound by a certain explicit number $f i (C(n, d))$ where $C(n, d)$ is a cyclic polytope and $f_{i}$ denotes the number of $i$-dimensional faces of the simplex. We say that $P$ is a polytope if it is the convex hull of a finite set of points in $\mathbb{R}^{d}$. Moreover, we say that $C(n, d)$ is a cyclic polytope if it is the convex hull of n distinct points on the moment curve $(t, t^{2},..., t{^d})$, $-\infty<t<\infty$. With this notation the Upper Bound Conjecture (for convex polytopes) states that cyclic polytope maximizes the number of $i$-dimensional faces among all polytopes.Zarzuela, Santiago2017info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/121133Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc-by-nc-nd (c) Catalin Dediu, 2017http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1211332026-05-27T06:46:51Z
dc.title.none.fl_str_mv On the proof of the upper bound theorem
title On the proof of the upper bound theorem
spellingShingle On the proof of the upper bound theorem
Dediu, Catalin
Àlgebra commutativa
Anells commutatius
Treballs de fi de màster
Geometria combinatòria
Commutative algebra
Commutative rings
Master's theses
Combinatorial geometry
title_short On the proof of the upper bound theorem
title_full On the proof of the upper bound theorem
title_fullStr On the proof of the upper bound theorem
title_full_unstemmed On the proof of the upper bound theorem
title_sort On the proof of the upper bound theorem
dc.creator.none.fl_str_mv Dediu, Catalin
author Dediu, Catalin
author_facet Dediu, Catalin
author_role author
dc.contributor.none.fl_str_mv Zarzuela, Santiago
dc.subject.none.fl_str_mv Àlgebra commutativa
Anells commutatius
Treballs de fi de màster
Geometria combinatòria
Commutative algebra
Commutative rings
Master's theses
Combinatorial geometry
topic Àlgebra commutativa
Anells commutatius
Treballs de fi de màster
Geometria combinatòria
Commutative algebra
Commutative rings
Master's theses
Combinatorial geometry
description Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2017, Director: Santiago Zarzuela
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/121133
url https://hdl.handle.net/2445/121133
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Catalin Dediu, 2017
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Catalin Dediu, 2017
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Màster Oficial - Matemàtica Avançada
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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