Combinatorics of 4-dimensional resultant polytopes
The Newton polytope of the resultant, or resultant polytope, characterizes the resultant polynomial more precisely than total degree. The combinatorics of resultant polytopes are known in the Sylvester case [5] and up to dimension 3 [9]. We extend this work by studying the combinatorial characteriza...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_97814503_v_n_p173_Dickenstein |
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todo:paper_97814503_v_n_p173_Dickenstein2023-10-03T16:43:17Z Combinatorics of 4-dimensional resultant polytopes Dickenstein, A. Emiris, I.Z. Fisikopoulos, V. F-vector Mixed subdivision Resultant Secondary polytope Cardinalities Classification results Combinatorics F vectors Mixed subdivision Newton polytopes Polytopes Resultant Algebra Combinatorial mathematics Vectors Topology The Newton polytope of the resultant, or resultant polytope, characterizes the resultant polynomial more precisely than total degree. The combinatorics of resultant polytopes are known in the Sylvester case [5] and up to dimension 3 [9]. We extend this work by studying the combinatorial characterization of 4-dimensional resultant polytopes, which show a greater diversity and involve computational and combinatorial challenges. In particular, our experiments, based on software respol for computing resultant polytopes, establish lower bounds on the maximal number of faces. By studying mixed subdivisions, we obtain tight upper bounds on the maximal number of facets and ridges, thus arriving at the following maximal f-vector: (22, 66, 66, 22), i.e. vector of face cardinalities. Certain general features emerge, such as the symmetry of the maximal f-vector, which are intriguing but still under investigation. We establish a result of independent interest, namely that the f-vector is maximized when the input supports are sufficiently generic, namely full dimensional and without parallel edges. Lastly, we offer a classification result of all possible 4-dimensional resultant polytopes. Copyright 2013 ACM. CONF info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_97814503_v_n_p173_Dickenstein |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
F-vector Mixed subdivision Resultant Secondary polytope Cardinalities Classification results Combinatorics F vectors Mixed subdivision Newton polytopes Polytopes Resultant Algebra Combinatorial mathematics Vectors Topology |
| spellingShingle |
F-vector Mixed subdivision Resultant Secondary polytope Cardinalities Classification results Combinatorics F vectors Mixed subdivision Newton polytopes Polytopes Resultant Algebra Combinatorial mathematics Vectors Topology Dickenstein, A. Emiris, I.Z. Fisikopoulos, V. Combinatorics of 4-dimensional resultant polytopes |
| topic_facet |
F-vector Mixed subdivision Resultant Secondary polytope Cardinalities Classification results Combinatorics F vectors Mixed subdivision Newton polytopes Polytopes Resultant Algebra Combinatorial mathematics Vectors Topology |
| description |
The Newton polytope of the resultant, or resultant polytope, characterizes the resultant polynomial more precisely than total degree. The combinatorics of resultant polytopes are known in the Sylvester case [5] and up to dimension 3 [9]. We extend this work by studying the combinatorial characterization of 4-dimensional resultant polytopes, which show a greater diversity and involve computational and combinatorial challenges. In particular, our experiments, based on software respol for computing resultant polytopes, establish lower bounds on the maximal number of faces. By studying mixed subdivisions, we obtain tight upper bounds on the maximal number of facets and ridges, thus arriving at the following maximal f-vector: (22, 66, 66, 22), i.e. vector of face cardinalities. Certain general features emerge, such as the symmetry of the maximal f-vector, which are intriguing but still under investigation. We establish a result of independent interest, namely that the f-vector is maximized when the input supports are sufficiently generic, namely full dimensional and without parallel edges. Lastly, we offer a classification result of all possible 4-dimensional resultant polytopes. Copyright 2013 ACM. |
| format |
CONF |
| author |
Dickenstein, A. Emiris, I.Z. Fisikopoulos, V. |
| author_facet |
Dickenstein, A. Emiris, I.Z. Fisikopoulos, V. |
| author_sort |
Dickenstein, A. |
| title |
Combinatorics of 4-dimensional resultant polytopes |
| title_short |
Combinatorics of 4-dimensional resultant polytopes |
| title_full |
Combinatorics of 4-dimensional resultant polytopes |
| title_fullStr |
Combinatorics of 4-dimensional resultant polytopes |
| title_full_unstemmed |
Combinatorics of 4-dimensional resultant polytopes |
| title_sort |
combinatorics of 4-dimensional resultant polytopes |
| url |
http://hdl.handle.net/20.500.12110/paper_97814503_v_n_p173_Dickenstein |
| work_keys_str_mv |
AT dickensteina combinatoricsof4dimensionalresultantpolytopes AT emirisiz combinatoricsof4dimensionalresultantpolytopes AT fisikopoulosv combinatoricsof4dimensionalresultantpolytopes |
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1782026182550618112 |