Tropical convex hulls of polyhedral sets
| Autor: | Hill, Cvetelina, Lamboglia, Sara, Simon, Faye Pasley |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we focus on the tropical convex hull of convex sets and polyhedral complexes. We give a vertex description of the tropical convex hull of a line segment and a ray. %in \RR^{n+1}/\RR\mathbf{1}. Next we show that tropical convex hull and ordinary convex hull commute in two dimensions and characterize tropically convex polyhedra in any dimension. %$\mathbb{R}^3/\mathbb {R}\mathbf{1}$. Finally we show that the dimension of a tropically convex fan depends on the coordinates of its rays and give a lower bound on the degree of a fan tropical curve using only tropical techniques. Comment: 12 pages, 3 Figures, New version with corrected proof of Theorem 1.10 and further results on tropically convex polyhedra |
| Databáze: | arXiv |
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