3 citations · 11 across the 18 of their papers we have counts for
21 papers
Complexes of strong discrete Morse matchings
Kevin Knudson, Abigail Owens-White
Using the strong discrete Morse theory developed by Fernández, we define the complex of strong discrete Morse matchings on a simplicial complex , as well as th…
Approximate triangulations of Grassmann manifolds
Kevin P. Knudson
We define the notion of an approximate triangulation for a manifold embedded in euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertic…
Min-max theory for cell complexes
Lacey Johnson, Kevin Knudson
In the study of smooth functions on manifolds, min-max theory provides a mechanism for identifying critical values of a function. In this paper we introduce a discretized version o…
Measuring Congressional District Meandering
Eion Blanchard, Kevin Knudson
In recent decades, state legislatures have often drawn U.S. Congressional voting districts that look---to the human eye---to be rather twisted. In this paper, we propose a method t…
Discrete Stratified Morse Theory: Algorithms and A User's Guide
Kevin Knudson, Bei Wang
Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete anal…
Theoretical Geometry, Critical Theory, and Concept Spaces in IR
Laura Sjoberg, Kevin Knudson
We use the theory of persistent homology to analyze a data set arising from the study of various aspects of democracy. Our results show that most "mature" democracies look more or…