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math.CO2023
Normality of -Matching Polytopes of Bipartite Graphs
Juan Camilo Torres
The -matching polytope of a graph is the convex hull of all its matchings of a given size when they are considered as indicator vectors. In this paper, we prove that the …
math.CO2021
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…
math.CO2020
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…