Polygons as sections of higher-dimensional polytopes

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Título:	Polygons as sections of higher-dimensional polytopes
Autor/a:	Padrol Sureda, Arnau; Pfeifle, Julián
Otros autores:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
Abstract:	We show that every heptagon is a section of a 3-polytope with 6 vertices. This implies that every n-gon with n >= 7 can be obtained as a section of a (2 + [n/7])-dimensional polytope with at most [6n/7] vertices; and provides a geometric proof of the fact that every nonnegative n x rn matrix of rank 3 has nonnegative rank not larger than [6min(n,m)/7]. This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122, 2014).
Abstract:	Peer Reviewed
Materia(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -polygon -polytope projections and sections -extension complexity -non-negative rank -nonrealizability -pseudo-line arrangements -Factorizations -Cone -Classificació AMS::05 Combinatorics
Derechos:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipo de documento:	Artículo - Versión publicada Artículo
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