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MiS Preprint

Computing Convex Hulls in the Affine Building of $SL_d$

Leon Zhang


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.

MSC Codes:
52, 05
tropical geometry, convex hulls, buildings

Related publications

2021 Repository Open Access
Leon Zhang

Computing min-convex hulls in the affine building of \(SL_d\)

In: Discrete and computational geometry, 65 (2021) 4, pp. 1314-1336