Many 2-Level Polytopes from Matroids
نویسندگان
چکیده
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·n−5/2 ·ρ−n, where c ≈ 0.03791727 and ρ−1 ≈ 4.88052854.
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 54 شماره
صفحات -
تاریخ انتشار 2015