10 citations · 34 across the 26 of their papers we have counts for
29 papers
Normal polytopes: between discrete, continuous, and random
Joseph Gubeladze
The first three sections of this survey represent an updated and much expanded version of the abstract of my talk at FPSAC'2010: new results are incorporated and several concrete c…
Bottom complexes
Joseph Gubeladze
The bottom complex of a finite polyhedal pointed rational cone is the lattice polytopal complex of the compact faces of the convex hull of nonzero lattice points in the cone. The a…
Normal polytopes and ellipsoids
Joseph Gubeladze
We show that: (1) unimodular simplices in a lattice 3-polytope cover a neighborhood of the boundary of the polytope if and only if the polytope is very ample, (2) the convex hull o…
The pyramidal growth
Joseph Gubeladze
Can one build an arbitrary polytope from any polytope inside by iteratively stacking pyramids onto facets, without losing the convexity throughout the process? We prove that this i…
Unimodular rows over monoid rings
Joseph Gubeladze
For a commutative Noetherian ring R of dimension d and a commutative cancellative monoid M, the elementary action on unimodular n-rows over the monoid ring R[M] is transitive for n…
Affine-compact functors
Joseph Gubeladze
Several well known polytopal constuctions are examined from the functorial point of view. A naive analogy between the Billera-Sturmfels fiber polytope and the abelian kernel is dis…