Symmetric Alcoved Polytopes

Details Symmetric Alcoved Polytopes Symmetric Alcoved Polytopes

2012-01-20

arxiv.org/abs/1201.4378v1

Mathematics

Combinatorics

12 pages

Scientific paper

Generalized alcoved polytopes are polytopes whose facet normals are roots in a given root system. We call a set of points in an alcoved polytope a generating set if there exists no strictly smaller alcoved polytope containing it. The type $A$ alcoved polytopes are precisely the convex polytopes that are also tropically convex. In this case the tropical generators form a generating set. We show that for any root system other than $F_4$, every alcoved polytpe invariant under the natural Weyl group action has a generating set of cardinality equal to the Coxeter number of the root system.

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