Tropical Halfspaces

Details Tropical Halfspaces Tropical Halfspaces

2003-12-02

arxiv.org/abs/math/0312068v3

Mathematics

Combinatorics

18 pages, 4 figures; v3: many new references, several minor changes, new layout, renumbering of the results

Scientific paper

As a new concept tropical halfspaces are introduced to the (linear algebraic) geometry of the tropical semiring (R,min,+). This yields exterior descriptions of the tropical polytopes that were recently studied by Develin and Sturmfels in a variety of contexts. The key tool to the understanding is a newly defined sign of the tropical determinant, which shares remarkably many properties with the ordinary sign of the determinant of a matrix. The methods are used to obtain an optimal tropical convex hull algorithm in two dimensions.

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