scholarly journals Coarsening polyhedral complexes

2012 ◽  
Vol 140 (10) ◽  
pp. 3593-3605
Author(s):  
Nathan Reading
Keyword(s):  
Polyhedral Complexes

scholarly journals Tropical ideals do not realise all Bergman fans

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Jan Draisma ◽  
Felipe Rincón
Keyword(s):  
Tropical Geometry ◽  
Tensor Products ◽  
Tropical Variety ◽  
Polyhedral Complex ◽  
Direct Sum ◽  
Weight One ◽  
Polyhedral Complexes

AbstractEvery tropical ideal in the sense of Maclagan–Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. This leads to the realisability question, ubiquitous in tropical geometry, of which weighted polyhedral complexes arise in this manner. Using work of Las Vergnas on the non-existence of tensor products of matroids, we prove that there is no tropical ideal whose variety is the Bergman fan of the direct sum of the Vámos matroid and the uniform matroid of rank two on three elements and in which all maximal cones have weight one.

scholarly journals Curvature Testing in 3-Dimensional Metric Polyhedral Complexes

2002 ◽  
Vol 11 (1) ◽  
pp. 143-158 ◽  
Author(s):  
Murray Elder ◽  
Jon McCammond
Keyword(s):  
3 Dimensional ◽  
Polyhedral Complexes

scholarly journals 3D well-composed polyhedral complexes

2015 ◽  
Vol 183 ◽  
pp. 59-77 ◽  
Author(s):  
Rocio Gonzalez-Diaz ◽  
Maria-Jose Jimenez ◽  
Belen Medrano
Keyword(s):  
Polyhedral Complexes

Modules of splines on polyhedral complexes

1992 ◽  
Vol 210 (1) ◽  
pp. 245-254 ◽  
Author(s):  
Sergey Yuzvinsky
Keyword(s):  
Polyhedral Complexes

scholarly journals Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images

2017 ◽  
Vol 59 (1) ◽  
pp. 106-122 ◽  
Author(s):  
Rocio Gonzalez-Diaz ◽  
Maria-Jose Jimenez ◽  
Belen Medrano
Keyword(s):  
Binary Images ◽  
Polyhedral Complexes

scholarly journals COMPLETIONS, REVERSALS, AND DUALITY FOR TROPICAL VARIETIES

2011 ◽  
Vol 10 (06) ◽  
pp. 1141-1163
Author(s):  
ZUR IZHAKIAN ◽  
LOUIS ROWEN
Keyword(s):  
Algebraic Structure ◽  
Tropical Geometry ◽  
Tropical Variety ◽  
Single Face ◽  
Polyhedral Complexes ◽  
Tropical Varieties

The object of this paper is to present two algebraic results with straightforward proofs, which have interesting consequences in tropical geometry. We start with an identity for polynomials over the max-plus algebra, which shows that any polynomial divides a product of binomials. Interpreted in tropical geometry, any tropical variety W can be completed to a union of tropical primitives, i.e. single-face polyhedral complexes. In certain situations, a tropical variety W has a "reversal" variety, which together with W already yields the union of primitives; this phenomenon is explained in terms of a map defined on the algebraic structure, and yields a duality on tropical hypersurfaces.

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