Computing Min-Convex Hulls in the Affine Building of $$\hbox {SL}_d$$SLd
2020
We describe an algorithm for computing the min-convex hull of a finite collection of points in the affine building of
$$\hbox {SL}_d(K)$$
, for K a field with discrete valuation. These min-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 min-convex hull as a tropical polytope.
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