47 citations · 95 across the 15 of their papers we have counts for
16 papers
Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala
Nathaniel K. Green, Edward D. Kim
We prove that the coefficient of in is a sum of squares in the entries of the symmetric matrices and .
On a polynomial positivity question of Collins, Dykema, and Torres-Ayala related to the Bessis-Moussa-Villani Conjecture
Edward D. Kim, Joe Miller, Laura Zinnel
We construct sum of squares certificates of non-negativity for two families of polynomials appearing as a variant by Collins, Dykema, and Torres-Ayala to Häegele's reformulation of…
Automatic Dynamic Parallelotope Bundles for Reachability Analysis of Nonlinear Systems
Edward Kim, Stanley Bak, Parasara Sridhar Duggirala
Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for disc…
Counterexamples to Siegel's Conjecture
Kean P. Fallon, Madisyn Janusiak, Edward D. Kim +1
We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.
Properties of the multiway discrepancy
Marianna Bolla, Edward Kim, Cheng Wai Koo
Some properties of the multiway discrepanc of rectangular matrices of nonnegative entries are discussed. We are able to prove the continuity of this discrepancy, as well as some st…
Tail diameter upper bounds for polytopes and polyhedra
J. Mackenzie Gallagher, Edward D. Kim
In 1992, Kalai and Kleitman proved a quasipolynomial upper bound on the diameters of convex polyhedra. Todd and Sukegawa-Kitahara proved tail-quasipolynomial bounds on the diameter…
An improved upper bound on the diameters of subset partition graphs
J. Mackenzie Gallagher, Edward D. Kim
In 1992, Kalai and Kleitman proved the first subexponential upper bound for the diameters of convex polyhedra. Eisenbrand et al. proved this bound holds for connected layer familie…
Non-archimedean connected Julia sets with branching
Dvij Bajpai, Robert L. Benedetto, Ruqian Chen +4
We construct the first examples of rational functions defined over a non-archimedean field with certain dynamical properties. In particular, we find such functions whose Julia sets…
Superlinear subset partition graphs with dimension reduction, strong adjacency, and endpoint count
Tristram C. Bogart, Edward D. Kim
We construct a sequence of subset partition graphs satisfying the dimension reduction, adjacency, strong adjacency, and endpoint count properties whose diameter has a superlinear a…
Combinatorics and Geometry of Transportation Polytopes: An Update
Jesús A. De Loera, Edward D. Kim
A transportation polytope consists of all multidimensional arrays or tables of non-negative real numbers that satisfy certain sum conditions on subsets of the entries. They arise n…
A note on the diameter of transportation polytopes with prescribed source degrees
Henning Bruhn-Fujimoto, Guillaume Chapuy, Edward D. Kim +1
Brightwell, van den Heuvel and Stougie proved that the diameter of an transportation polytope is at most , a factor of eight away from the Hirsch Conjecture.…
Polyhedral graph abstractions and an approach to the Linear Hirsch Conjecture
Edward D. Kim
We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of p…
Geometric Combinatorics of Transportation Polytopes and the Behavior of the Simplex Method
Edward D. Kim
This dissertation investigates the geometric combinatorics of convex polytopes and connections to the behavior of the simplex method for linear programming. We focus our attention…
Companion to "An update on the Hirsch conjecture"
Edward D. Kim, Francisco Santos
This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.
An update on the Hirsch conjecture
Edward D. Kim, Francisco Santos
The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter…
Graphs of Transportation Polytopes
Jesús A. De Loera, Edward D. Kim, Shmuel Onn +1
This paper discusses properties of the graphs of 2-way and 3-way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results i…