Isocanted alcoved polytopes

María Jesús de la Puente; Pedro Luis Clavería

Applications of Mathematics (2020)

  • Volume: 65, Issue: 6, page 703-726
  • ISSN: 0862-7940

Abstract

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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 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 ⌋ .

How to cite

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de la Puente, María Jesús, and Clavería, Pedro Luis. "Isocanted alcoved polytopes." Applications of Mathematics 65.6 (2020): 703-726. <http://eudml.org/doc/296940>.

@article{delaPuente2020,
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, $3^d$, 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 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 $\lfloor d/3\rfloor $.},
author = {de la Puente, María Jesús, Clavería, Pedro Luis},
journal = {Applications of Mathematics},
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},
language = {eng},
number = {6},
pages = {703-726},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Isocanted alcoved polytopes},
url = {http://eudml.org/doc/296940},
volume = {65},
year = {2020},
}

TY - JOUR
AU - de la Puente, María Jesús
AU - Clavería, Pedro Luis
TI - Isocanted alcoved polytopes
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 6
SP - 703
EP - 726
AB - 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 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 $\lfloor d/3\rfloor $.
LA - eng
KW - 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
UR - http://eudml.org/doc/296940
ER -

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