Positive Plücker tree certificates for non-realizability
| Autor: | Pfeifle, Julián |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
| Rok vydání: | 2022 |
| Předmět: |
14 Algebraic geometry::14M Special varieties [Classificació AMS]
Polytopes 52 Convex and discrete geometry::52B Polytopes and polyhedra [Classificació AMS] General Mathematics Integer programming Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC] Programació en nombres enters 90 Operations research mathematical programming::90C Mathematical programming [Classificació AMS] Politops |
| Zdroj: | Experimental Mathematics. :1-17 |
| ISSN: | 1944-950X 1058-6458 |
| DOI: | 10.1080/10586458.2021.1994487 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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