Positive Plücker tree certificates for non-realizability
We introduce a new method for finding a non-realizability certificate of a simplicial sphere S: we exhibit a monomial combination of classical 3-term Pl¨ucker relations that yields a sum of products of determinants that are known to be positive in any realization of S; but their sum should vanish, c...
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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/381204 |
| Acesso em linha: | https://hdl.handle.net/2117/381204 https://dx.doi.org/10.1080/10586458.2021.1994487 |
| Access Level: | acceso abierto |
| Palavra-chave: | Polytopes Integer programming Politops Programació en nombres enters Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming Classificació AMS::14 Algebraic geometry::14M Special varieties Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Resumo: | We introduce a new method for finding a non-realizability certificate of a simplicial sphere S: we exhibit a monomial combination of classical 3-term Pl¨ucker relations that yields a sum of products of determinants that are known to be positive in any realization of S; but their sum should vanish, contradiction. Using this technique, we prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere constructed by Zheng, a family of highly neighborly centrally symmetric spheres constructed by by Novik and Zheng, and several combinatorial prismatoids introduced by Criado and Santos. The method in fact works for orientable pseudo-manifolds, not just for spheres. |
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