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arXiv · 1707.02814

Multi-splits and tropical linear spaces from nested matroids

Benjamin Schröter
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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.

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Benjamin Schröter. 2017-07-10. Multi-splits and tropical linear spaces from nested matroids. https://doi.org/10.1007/s00454-018-0021-1

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