Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
2021-09
We introduce a new method for finding a non-realizability certificate of a simplicial sphere S. It enables us to prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere by Zheng, a family of highly neighborly centrally symmetric spheres by Novik and Zheng, and several combinatorial prismatoids introduced by Criado and Santos. The method, implemented in the polymake framework, uses integer programming to find a monomial combination of classical 3-term Plücker relations that must be positive in any realization of S; but since this combination should also vanish identically, the realization cannot exist. Previous approaches by Firsching, implemented using SCIP, and by Gouveia, Macchia and Wiebe, implemented using Singular and Macaulay2, are not able to process these examples.
Peer Reviewed
Postprint (author's final draft)
Article
Anglès
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica; Integer programming; Programació en nombres enters; Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming; Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra
https://dl.acm.org/doi/10.1145/3511528.3511533
Open Access
E-prints [72986]
