10 citations · 34 across the 26 of their papers we have counts for
11 papers · 1 filter
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…
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…
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…
The poset of rational cones
Joseph Gubeladze, Mateusz Michałek
We introduce a natural partial order on the set Cones(d) of rational cones in R^d. The poset NPol(d-1) of normal polytopes in R^{d-1} embeds into Cones(d) via the homogenization ma…
Quantum jumps of normal polytopes
Winfried Bruns, Joseph Gubeladze, Mateusz Michałek
We introduce a partial order on the set of all normal polytopes in R^d. This poset NPol(d) is a natural discrete counterpart of the continuum of convex compact sets in R^d, ordered…
Very ample and Koszul segmental fibrations
Matthias Beck, Jessica Delgado, Joseph Gubeladze +1
In the hierarchy of structural sophistication for lattice polytopes, normal polytopes mark a point of origin; very ample and Koszul polytopes occupy bottom and top spots in this hi…
Vertex maps between simplices, cubes, and crosspolytopes
Joseph Gubeladze, Jack Love
We study the vertices of the polytopes of all affine maps (a.k.a. hom-polytopes) between higher dimensional simplices, cubes, and crosspolytopes. Systematic study of general hom-po…
Hom-polytopes
Tristram Bogart, Mark Contois, Joseph Gubeladze
We study the polytopes of affine maps between two polytopes -- the hom-polytopes. The hom-polytope functor has a left adjoint -- tensor product polytopes. The analogy with the cate…
Convex normality of rational polytopes with long edges
Joseph Gubeladze
We introduce the property of convex normality of rational polytopes and give a dimensionally uniform lower bound for the edge lattice lengths, guaranteeing the property. As an appl…
Unimodular covers of multiples of polytopes
Winfried Bruns, Joseph Gubeladze
Let P be a d-dimensional lattice polytope. We show that there exists a natural number c_d, only depending on d, such that the multiples cP have a unimodular cover for every natural…