Isocanted alcoved polytopes [article]

María Jesús de la Puente
2020 arXiv   pre-print
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
more » ... is the lattice of proper subsets of [d+1] and its diameter is d+1. They are realizations of d–elementary cubical polytopes. The f–vector of a d–dimensional isocanted alcoved polytope attains its maximum at the integer ⌊ d/3⌋.
arXiv:2009.13858v1 fatcat:v764dqzwrre5fjhk2npaumoe4a