10 papers
The phase rank of a matrix
António Pedro Goucha, João Gouveia
In this paper, we introduce and study the notion of phase rank. Given a matrix filled with phases, i.e., with complex entries of modulus , its phase rank is the smallest possibl…
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…
On sums of squares of -nomials
João Gouveia, Alexander Kovačec, Mina Saee
In 2005, Boman et al introduced the concept of factor width for a real symmetric positive semidefinite matrix. This is the smallest positive integer for which the matrix ca…