dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
dc.contributor.author
Pfeifle, Julián
dc.identifier
Pfeifle, J. Large final polynomials from integer programming. "ACM COMMUNICATIONS IN COMPUTER ALGEBRA", Setembre 2021, vol. 55, núm. 3, p. 82-86.
dc.identifier
https://hdl.handle.net/2117/362955
dc.identifier
10.1145/3511528.3511533
dc.description.abstract
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.
dc.description.abstract
Peer Reviewed
dc.description.abstract
Postprint (author's final draft)
dc.format
application/pdf
dc.relation
https://dl.acm.org/doi/10.1145/3511528.3511533
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
dc.subject
Integer programming
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Programació en nombres enters
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Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
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Classificació AMS::52 Convex and discrete geometry::52B Polytopes and polyhedra
dc.title
Large final polynomials from integer programming
