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 does not exist a strictly smaller alcoved polytope containing it. The type $A$ alcoved polytopes are precisely the tropical polytopes that are also convex in the usual sense. In this case the tropical generators form a generating set. We show that for any root system other than $F_4$, every alcoved polytope invariant under the natural Weyl group action has a generating set of cardinality equal to the Coxeter number of the root system.
@article{10_37236_3646,
author = {Annette Werner and Josephine Yu},
title = {Symmetric alcoved polytopes},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/3646},
zbl = {1302.52014},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3646/}
}
TY - JOUR
AU - Annette Werner
AU - Josephine Yu
TI - Symmetric alcoved polytopes
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/3646/
DO - 10.37236/3646
ID - 10_37236_3646
ER -
