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math.CO2026
Two Linear Programs are Better than One
Alexander E. Black, Christoph Hertrich, Stefan Kober +1
The extension complexity of a polytope is the minimum number of facets of a polytope that projects onto it. Motivated by the complexity of neural network…
math.CO2026
Monotone Diameters of Lattice Polytopes
Alexander E. Black
An influential 1989 result of Naddef shows that the diameters of -polytopes are at most their dimension. This was extended shortly after by Kleinschmidt and Onn to any lattice…
math.CO2026
Any Proof of Polynomial Hirsch Must be Completely Incoherent
Alexander E. Black, Lei Xue
In 1992, Billera and Sturmfels introduced coherent monotone paths on polytopes as part of their description of the fiber polytope construction, and later in 1994 showed with Kapran…