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.
Computing Convex Hulls in the Affine Building of SL_d
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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.
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2019 1verdicts
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Tropical Ehrhart Theory and Tropical Volume
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.