Computing Convex Hulls in the Affine Building of SL_d

2018/11/21 by Leon Zhang, Zhang, Leon
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG

paper · pdf · doi:10.48550/arxiv.1811.08884

18 pages, 11 figures

arxiv created 2018/11/21 · arxiv updated 2018/11/22

Abstract

We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls describe the relations among a finite collection of invertible matrices over K. As a consequence, we bound the dimension of the tropical projective space needed to realize the convex hull as a tropical polytope.

Related

• Tropical Convex Hull Computations
• Convex hulls of finite sets of points in two and three dimensions
• Convex Hull Calculations: a Matlab Implementation and Correctness Proofs for the lrs-Algorithm
• Non-elliptic Webs and Convex Sets in the Affine Building
• Convex hull lattices point generated