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Title:	Many 2-level polytopes from matroids
Author:	Grande, Francesco; Rué Perna, Juan José
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques
Abstract:	The final publication is available at Springer via DOI 10.1007/s00454-015-9735-5
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.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Combinatorial analysis -matroid theory -2-level polytopes -analytic combinatorics -asymptotic enumeration -Anàlisi combinatòria
Rights:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
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