2 citations · 2 across the 8 of their papers we have counts for
12 papers
Matrices of nonnegative integer rank two
João Gouveia, Amy Wiebe
The nonnegative integer rank of a matrix is a variant of the classical nonnegative rank, introduced in the 1980s, where factorizations are required to have integer entries. While c…
A Yannakakis-type theorem for lifts of affine semigroups
João Gouveia, Amy Wiebe
Yannakakis' theorem relating the extension complexity of a polytope to the size of a nonnegative factorization of its slack matrix is a seminal result in the study of lifts of conv…
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…
Combinatorial Methods for Minkowski Tensors of Polytopes
Niklas Livchitz, Büşra Sert, Amy Wiebe
In this paper we use a generating function approach to record and calculate entries of the Minkowski tensors of a polytope. We focus on ''surface tensors'', extending the methods u…
Slack Ideals in Macaulay2
Antonio Macchia, Amy Wiebe
Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matri…
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 matroid
Madeline Brandt, Amy Wiebe
We introduce a new model for the realization space of a matroid, which is obtained from a variety defined by a saturated determinantal ideal, called the slack ideal, coming from th…
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…
Large sets of complex and real equiangular lines
Jonathan Jedwab, Amy Wiebe
Large sets of equiangular lines are constructed from sets of mutually unbiased bases, over both the complex and the real numbers.
Constructions of complex equiangular lines from mutually unbiased bases
Jonathan Jedwab, Amy Wiebe
A set of vectors of equal norm in represents equiangular lines if the magnitudes of the Hermitian inner product of every pair of distinct vectors in the set are equa…
A simple construction of complex equiangular lines
Jonathan Jedwab, Amy Wiebe
A set of vectors of equal norm in represents equiangular lines if the magnitudes of the inner product of every pair of distinct vectors in the set are equal. The max…