3 citations · 3 across the 5 of their papers we have counts for
10 papers
Bounds on Determinantal Complexity of Two Types of Generalized Permanents
Tristram Bogart, Juan Andrés Valero
We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permane…
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…
A Plethora of Polynomials: A Toolbox for Counting Problems
Tristram Bogart, Kevin Woods
A wide variety of problems in combinatorics and discrete optimization depend on counting the set of integer points in a polytope, or in some more general object constructed via…
Constructing Partial MDS Codes from Reducible Curves
Tristram Bogart, Anna-Lena Horlemann-Trautmann, David Karpuk +2
We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and im…
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…
Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic
Tristram Bogart, John Goodrick, Kevin Woods
Let be polynomial functions of . For fixed , let be the numerical semigroup generated by $f_1(n),\ldots,f_k(n)…