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Computing Convex Hulls in the Affine Building of SL_d

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arxiv 1811.08884 v1 pith:QOFSIJLU submitted 2018-11-21 math.CO math.MG

Leon Zhang This is my paper · ORCID
classification math.COmath.MG
keywords convexaffinebuildingcollectioncomputingdescribefinitehull
verification ladder T0 review T1 audit T2 compute T3 formal

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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.

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  1. Tropical Ehrhart Theory and Tropical Volume

    math.MG 2019-08 accept novelty 7.0 of 10

    A new tropical volume, called the tropical barycentric volume, is defined from a tropical Ehrhart polynomial and is shown to satisfy the standard volume axioms and to be upper bounded by the dequantized tropical volume.

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