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DC Field | Value | Language |
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dc.contributor.advisor | Zarzuela, Santiago | - |
dc.contributor.author | Dediu, Catalin | - |
dc.date.accessioned | 2018-03-27T08:25:51Z | - |
dc.date.available | 2018-03-27T08:25:51Z | - |
dc.date.issued | 2017-09-09 | - |
dc.identifier.uri | http://hdl.handle.net/2445/121133 | - |
dc.description | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2017, Director: Santiago Zarzuela | ca |
dc.description.abstract | [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. | ca |
dc.format.extent | 58 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-nc-nd (c) Catalin Dediu, 2017 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | - |
dc.source | Màster Oficial - Matemàtica Avançada | - |
dc.subject.classification | Àlgebra commutativa | cat |
dc.subject.classification | Anells commutatius | cat |
dc.subject.classification | Treballs de fi de màster | cat |
dc.subject.classification | Geometria combinatòria | ca |
dc.subject.other | Commutative algebra | eng |
dc.subject.other | Commutative rings | eng |
dc.subject.other | Master's theses | eng |
dc.subject.other | Combinatorial geometry | en |
dc.title | On the proof of the upper bound theorem | ca |
dc.type | info:eu-repo/semantics/masterThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
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File | Description | Size | Format | |
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memoria.pdf | Memòria | 829.89 kB | Adobe PDF | View/Open |
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