Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/113917
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Gouveia, João | - |
dc.contributor.author | Macchia, Antonio | - |
dc.contributor.author | Wiebe, Amy | - |
dc.date.accessioned | 2024-03-11T09:34:07Z | - |
dc.date.available | 2024-03-11T09:34:07Z | - |
dc.date.issued | 2022 | - |
dc.identifier.issn | 0179-5376 | pt |
dc.identifier.issn | 1432-0444 | pt |
dc.identifier.uri | https://hdl.handle.net/10316/113917 | - |
dc.description.abstract | In this paper we examine four different models for the realization space of a polytope: the classical model, the Grassmannian model, the Gale transform model, and the slack variety. Respectively, they identify realizations of the polytopes with the matrix whose columns are the coordinates of their vertices, the column space of said matrix, their Gale transforms, and their slack matrices. Each model has been used to study realizations of polytopes. In this paper we establish very explicitly the maps that allow us to move between models, study their precise relationships, and combine the strengths of different viewpoints. As an illustration, we combine the compact nature of the Grassmannian model with the slack variety to obtain a reduced slack model that allows us to perform slack ideal calculations that were previously out of computational reach. These calculations allow us to answer the question of Criado and Santos (Exp. Math. (2019). https://doi.org/10.1080/10586458.2019.1641766), about the realizability of a family of prismatoids, in general in the negative by proving the non-realizability of one of them. | pt |
dc.language.iso | eng | pt |
dc.publisher | Springer Nature | pt |
dc.rights | openAccess | pt |
dc.subject | Polytopes | pt |
dc.subject | Cones | pt |
dc.subject | Realization spaces | pt |
dc.subject | Grassmannian | pt |
dc.subject | Slack matrix | pt |
dc.subject | Slack ideal | pt |
dc.subject | Gale transforms | pt |
dc.title | Combining Realization Space Models of Polytopes | pt |
dc.type | article | - |
degois.publication.firstPage | 505 | pt |
degois.publication.lastPage | 542 | pt |
degois.publication.issue | 2 | pt |
degois.publication.title | Discrete and Computational Geometry | pt |
dc.peerreviewed | yes | pt |
dc.identifier.doi | 10.1007/s00454-022-00379-8 | pt |
degois.publication.volume | 69 | pt |
dc.date.embargo | 2022-01-01 | * |
uc.date.periodoEmbargo | 0 | pt |
item.openairetype | article | - |
item.fulltext | Com Texto completo | - |
item.languageiso639-1 | en | - |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0001-8345-9754 | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais FCTUC Matemática - Artigos em Revistas Internacionais |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Combining-Realization-Space-Models-of-PolytopesDiscrete-and-Computational-Geometry.pdf | 756.83 kB | Adobe PDF | View/Open |
Page view(s)
37
checked on Jul 17, 2024
Download(s)
10
checked on Jul 17, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.