3 papers
math.CO2023
Sampling planar tanglegrams and pairs of disjoint triangulations
Alexander E. Black, Kevin Liu, Alex Mcdonough +4
A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that th…
math.OC2022
Small Shadows of Lattice Polytopes
Alexander E. Black
The diameter of the graph of a -dimensional lattice polytope is known to be at most due to work by Kleinschmidt and Onn. However, it is an open ques…
math.CO2022
The Polyhedral Geometry of Pivot Rules and Monotone Paths
Alexander E. Black, Jesús A. De Loera, Niklas Lütjeharms +1
Motivated by the analysis of the performance of the simplex method we study the behavior of families of pivot rules of linear programs. We introduce normalized-weight pivot rules w…