Many 2-level polytopes from matroids

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/85655

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor.author	Grande, Francesco
dc.contributor.author	Rué Perna, Juan José
dc.date	2015-10-26
dc.identifier.citation	Grande, F., Rue, J. Many 2-level polytopes from matroids. "Discrete and computational geometry", 26 Octubre 2015, vol. 54, núm. 3, p. 954-979.
dc.identifier.citation	0179-5376
dc.identifier.citation	10.1007/s00454-015-9735-5
dc.identifier.uri	http://hdl.handle.net/2117/85655
dc.language.iso	eng
dc.relation	info:eu-repo/grantAgreement/EC/FP7/630749/EU/Enumeration of discrete structures: algebraic, analytic, probabilistic and algorithmic methods for enriched planar graphs and planar maps/COUNTGRAPH
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Combinatorial analysis
dc.subject	matroid theory
dc.subject	2-level polytopes
dc.subject	analytic combinatorics
dc.subject	asymptotic enumeration
dc.subject	Anàlisi combinatòria
dc.title	Many 2-level polytopes from matroids
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	The final publication is available at Springer via DOI 10.1007/s00454-015-9735-5
dc.description.abstract	The family of 2-level matroids, that is, matroids whose base polytope is 2-level, has been recently studied and characterized by means of combinatorial properties. 2-Level matroids generalize series-parallel graphs, which have been already successfully analyzed from the enumerative perspective. We bring to light some structural properties of 2-level matroids and exploit them for enumerative purposes. Moreover, the counting results are used to show that the number of combinatorially non-equivalent (n-1)(n-1)-dimensional 2-level polytopes is bounded from below by c·n-5/2·¿-nc·n-5/2·¿-n, where c˜0.03791727c˜0.03791727 and ¿-1˜4.88052854¿-1˜4.88052854.

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