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| dc.contributor | Zarzuela, Santiago | |
| dc.creator | Dediu, Catalin | |
| dc.date | 2018-03-27T08:25:51Z | |
| dc.date | 2018-03-27T08:25:51Z | |
| dc.date | 2017-09-09 | |
| dc.date.accessioned | 2024-12-16T10:26:20Z | |
| dc.date.available | 2024-12-16T10:26:20Z | |
| dc.identifier | http://hdl.handle.net/2445/121133 | |
| dc.identifier.uri | http://fima-docencia.ub.edu:8080/xmlui/handle/123456789/20938 | |
| dc.description | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2017, Director: Santiago Zarzuela | |
| dc.description | [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. | |
| dc.format | 58 p. | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.rights | cc-by-nc-nd (c) Catalin Dediu, 2017 | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.source | Màster Oficial - Matemàtica Avançada | |
| dc.subject | Àlgebra commutativa | |
| dc.subject | Anells commutatius | |
| dc.subject | Treballs de fi de màster | |
| dc.subject | Geometria combinatòria | |
| dc.subject | Commutative algebra | |
| dc.subject | Commutative rings | |
| dc.subject | Master's theses | |
| dc.subject | Combinatorial geometry | |
| dc.title | On the proof of the upper bound theorem | |
| dc.type | info:eu-repo/semantics/masterThesis |
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