Séminaire Lotharingien de Combinatoire, 93B.158 (2025), 12 pp.
Nick Early, Lukas Kühne, and Leonid Monin
Minkowski Decompositions of Alcoved Polytopes
Abstract.
We develop a systematic theory of Minkowski sum decompositions for alcoved polytopes, a family of convex polytopes whose facet normals are parallel to roots of type A. Our main result establishes that the type fan of alcoved polytopes is two-determined: the Minkowski sum of a collection of alcoved polytopes is alcoved if and only if each pairwise sum is alcoved. We provide a complete characterization of compatibility between alcoved simplices via a graphical criterion on ordered set partitions that remarkably reduces to conditions on subsequences of length at most six.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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