Multi-splits and tropical linear spaces from nested matroids
arXiv:1707.02814 · doi:10.1007/s00454-018-0021-1
Abstract
In this paper we present an explicit combinatorial description of a special class of facets of the secondary polytopes of hypersimplices. These facets correspond to polytopal subdivisions called multi-splits. We show a relation between the cells in a multi-split of the hypersimplex and nested matroids. Moreover, we get a description of all multi-splits of a product of simplices. Additionally, we present a computational result to derive explicit lower bounds on the number of facets of secondary polytopes of hypersimplices.
21 pages, 4 figures, 2 tables