polyhedral combinatorics
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Author(s):  
Helen Naumann ◽  
Thorsten Theobald

AbstractSublinear circuits are generalizations of the affine circuits in matroid theory, and they arise as the convex-combinatorial core underlying constrained non-negativity certificates of exponential sums and of polynomials based on the arithmetic-geometric inequality. Here, we study the polyhedral combinatorics of sublinear circuits for polyhedral constraint sets. We give results on the relation between the sublinear circuits and their supports and provide necessary as well as sufficient criteria for sublinear circuits. Based on these characterizations, we provide some explicit results and enumerations for two prominent polyhedral cases, namely the non-negative orthant and the cube [− 1,1]n.



2017 ◽  
Vol 216 ◽  
pp. 321-322
Author(s):  
Valentin E. Brimkov ◽  
Reneta P. Barneva


2016 ◽  
Vol 211 ◽  
pp. 1-14 ◽  
Author(s):  
Zacharie Ales ◽  
Arnaud Knippel ◽  
Alexandre Pauchet


2013 ◽  
Vol 50 (2) ◽  
pp. 327-338 ◽  
Author(s):  
Ruth Davidson ◽  
Seth Sullivant




4OR ◽  
2006 ◽  
Vol 4 (1) ◽  
pp. 29-46
Author(s):  
Matthias Jach ◽  
Matthias Köppe ◽  
Robert Weismantel


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