2003/12/02 by Michael Joswig, Joswig, Michael
Mathematics · #06A07 #52B99 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG #msc:06A07 #msc:52B99
paper · pdf · doi:10.48550/arxiv.math/0312068
18 pages, 4 figures; v3: many new references, several minor changes, new layout, renumbering of the results
arxiv created 2004/08/24 · arxiv updated 2009/12/01
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.