Abstract
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, 3d, 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 2d+1 − 2 vertices, its face lattice 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⌋.
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We thank the referee for careful revision.
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The first author is partially supported by Ministerio de Economía y Competitividad, Proyecto I+D MTM2016-76808-P, Ministerio de Ciencia e Innovación, Proyecto PID-2019-10770 GB-I00 and by UCM research group 910444.
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de la Puente, M.J., Clavería, P.L. Isocanted Alcoved Polytopes. Appl Math 65, 703–726 (2020). https://doi.org/10.21136/AM.2020.0373-19
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DOI: https://doi.org/10.21136/AM.2020.0373-19
Keywords
- cubical polytope
- isocanted
- alcoved
- centrally symmetric
- almost simple
- zonotope
- f-vector
- cubical g-vector
- unimodal
- flag
- face lattice
- log-concave sequence
- tropical normal idempotent matrix
- symmetric matrix