124 citations · 361 across the 23 of their papers we have counts for
8 papers · 1 filter
Complex psd-minimal polytopes in dimensions two and three
Tristram Bogart, João Gouveia, Juan Camilo Torres
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real se…
General non-realizability certificates for spheres with linear programming
Joao Gouveia, Antonio Macchia, Amy Wiebe
In this paper we present a simple technique to derive certificates of non-realizability for an abstract polytopal sphere. Our approach uses a variant of the classical algebraic cer…
An Algebraic Approach to Projective Uniqueness with an Application to Order Polytopes
Tristram Bogart, João Gouveia, Juan Camilo Torres
A combinatorial polytope is said to be projectively unique if it has a single realization up to projective transformations. Projective uniqueness is a geometrically compelling…
Combining realization space models of polytopes
João Gouveia, Antonio Macchia, Amy Wiebe
In this paper we examine four different models for the realization space of a polytope: the classical model, the Grassmannian model, the Gale transform model, and the slack variety…
Projectively unique polytopes and toric slack ideals
João Gouveia, Antonio Macchia, Rekha R. Thomas +1
The slack ideal of a polytope is a saturated determinantal ideal that gives rise to a new model for the realization space of the polytope. The simplest slack ideals are toric and h…
The Slack Realization Space of a Polytope
João Gouveia, Antonio Macchia, Rekha R. Thomas +1
In this paper we introduce a natural model for the realization space of a polytope up to projective equivalence which we call the slack realization space of the polytope. The model…
On ranks of regular polygons
António Pedro Goucha, João Gouveia, Pedro M. Silva
In this paper we study various versions of extension complexity for polygons through the study of factorization ranks of their slack matrices. In particular, we develop a new asymp…
Four Dimensional Polytopes of Minimum Positive Semidefinite Rank
João Gouveia, Kanstanstin Pashkovich, Richard Z. Robinson +1
The positive semidefinite (psd) rank of a polytope is the size of the smallest psd cone that admits an affine slice that projects linearly onto the polytope. The psd rank of a d-po…