scholarly journals Tropical realization spaces for polyhedral complexes

2013 ◽  
pp. 235-251 ◽  
Author(s):  
Eric Katz
Keyword(s):  
Realization Spaces ◽  
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 Realization Spaces of Arrangements of Convex Bodies

2017 ◽  
Vol 58 (1) ◽  
pp. 1-29
Author(s):  
Michael Gene Dobbins ◽  
Andreas Holmsen ◽  
Alfredo Hubard
Keyword(s):  
Convex Bodies ◽  
Realization Spaces

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

scholarly journals ON THE DIMENSIONS OF THE REALIZATION SPACES OF POLYTOPES

Mathematika ◽  
2021 ◽  
Vol 67 (2) ◽  
pp. 342-365
Author(s):  
Laith Rastanawi ◽  
Rainer Sinn ◽  
Günter M. Ziegler
Keyword(s):  
Realization Spaces
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