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Isocanted alcoved polytopes

María Jesús de la Puente; Pedro Luis Clavería — 2020

Applications of Mathematics

Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their $f$ -vectors and checking the validity of the following five conjectures: Bárány, unimodality, $3^{d}$ , flag and cubical lower bound (CLBC). Isocanted alcoved polytopes are centrally symmetric, almost simple cubical polytopes. They are zonotopes. We show that, for each dimension, there is a unique combinatorial type. In dimension $d$ , an isocanted alcoved polytope has $2^{d + 1} - 2$ vertices, its face lattice is the lattice...

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