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math.CO2024
Random Shadows of Fixed Polytopes
Alexander E. Black, Francisco Criado
Estimating the number of vertices of a two dimensional projection, called a shadow, of a polytope is a fundamental tool for understanding the performance of the shadow simplex meth…
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.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…