Geodesic
Isocanted alcoved polytopes
Applications of Mathematics, Tome 65 (2020) no. 6, pp. 703-726.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $.
DOI : 10.21136/AM.2020.0373-19
Classification : 15A80, 52B12
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 
@article{10_21136_AM_2020_0373_19,
     author = {de la Puente, Mar{\'\i}a Jes\'us and Claver{\'\i}a, Pedro Luis},
     title = {Isocanted alcoved polytopes},
     journal = {Applications of Mathematics},
     pages = {703--726},
     publisher = {mathdoc},
     volume = {65},
     number = {6},
     year = {2020},
     doi = {10.21136/AM.2020.0373-19},
     mrnumber = {4191365},
     zbl = {07285953},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0373-19/}
}
TY  - JOUR
AU  - de la Puente, María Jesús
AU  - Clavería, Pedro Luis
TI  - Isocanted alcoved polytopes
JO  - Applications of Mathematics
PY  - 2020
SP  - 703
EP  - 726
VL  - 65
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0373-19/
DO  - 10.21136/AM.2020.0373-19
LA  - en
ID  - 10_21136_AM_2020_0373_19
ER  - 
%0 Journal Article
%A de la Puente, María Jesús
%A Clavería, Pedro Luis
%T Isocanted alcoved polytopes
%J Applications of Mathematics
%D 2020
%P 703-726
%V 65
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0373-19/
%R 10.21136/AM.2020.0373-19
%G en
%F 10_21136_AM_2020_0373_19
de la Puente, María Jesús; Clavería, Pedro Luis. Isocanted alcoved polytopes. Applications of Mathematics, Tome 65 (2020) no. 6, pp. 703-726. doi : 10.21136/AM.2020.0373-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0373-19/

Cité par Sources :