Year: 2014
Type: preprint
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)-dimensional 2-level polytopes is bounded from below by $c \cdot n^{-5/2} \cdot ρ^{-n}$, where $c\approx 0.03791727 $ and $ρ^{-1} \approx 4.88052854$.
Source: arXiv (Cornell University)
Authors: Grande, Francesco, Rué, Juanjo
Institution: Freie Universität Berlin
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950021746