Computing min-convex hulls in the affine building of \(\mathrm{SL}_d\). (English) Zbl 1473.52023
Let \(K\) be a field with a discrete valuation. The author describes an algorithm for computing the min-convex hull of a finite collection of points in the affine building of the group SL\(_d (K)\). This min-convex hull can be realized as a tropical polytope, and the author’s algorithm provides a bound for the dimension of the tropical projective space where this realization takes place. This is an improvement about other existing algorithms, and makes it feasible to compute min-convex hulls in practice for the first time.
Reviewer: Norbert Knarr (Stuttgart)
MSC:
| 52B55 | Computational aspects related to convexity |
| 05E45 | Combinatorial aspects of simplicial complexes |
| 14T20 | Geometric aspects of tropical varieties |
| 51E24 | Buildings and the geometry of diagrams |
Software:
polymakeReferences:
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