| Title:
|
Isocanted alcoved polytopes (English) |
| Author:
|
de la Puente, María Jesús |
| Author:
|
Clavería, Pedro Luis |
| Language:
|
English |
| Journal:
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Applications of Mathematics |
| ISSN:
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0862-7940 (print) |
| ISSN:
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1572-9109 (online) |
| Volume:
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65 |
| Issue:
|
6 |
| Year:
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2020 |
| Pages:
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703-726 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $. (English) |
| Keyword:
|
cubical polytope |
| Keyword:
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isocanted |
| Keyword:
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alcoved |
| Keyword:
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centrally symmetric |
| Keyword:
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almost simple |
| Keyword:
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zonotope |
| Keyword:
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$f$-vector |
| Keyword:
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cubical $g$-vector |
| Keyword:
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unimodal |
| Keyword:
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flag |
| Keyword:
|
face lattice |
| Keyword:
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log-concave sequence |
| Keyword:
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tropical normal idempotent matrix |
| Keyword:
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symmetric matrix |
| MSC:
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15A80 |
| MSC:
|
52B12 |
| idZBL:
|
Zbl 07285953 |
| idMR:
|
MR4191365 |
| DOI:
|
10.21136/AM.2020.0373-19 |
| . |
| Date available:
|
2020-11-18T09:36:52Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148392 |
| . |
| Reference:
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