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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
99/2018

Computing Convex Hulls in the Affine Building of $SL_d$

Leon Zhang

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.

Received:
Nov 23, 2018
Published:
Nov 23, 2018
MSC Codes:
52, 05
Keywords:
tropical geometry, convex hulls, buildings

Related publications

inJournal
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