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Full-Text Articles in Physical Sciences and Mathematics
Relationships Between Braid Length And The Number Of Braid Strands, Cornelia A. Van Cott
Relationships Between Braid Length And The Number Of Braid Strands, Cornelia A. Van Cott
Mathematics
For a knot K, let ℓ(K,n) be the minimum length of an n–stranded braid representative of K. Fixing a knot K, ℓ(K,n) can be viewed as a function of n, which we denote by ℓK(n). Examples of knots exist for which ℓK(n) is a nonincreasing function. We investigate the behavior of ℓK(n), developing bounds on the function in terms of the genus of K. The bounds lead to the conclusion that for any knot K the function ℓK(n) is eventually stable. We study the stable behavior of ℓK(n), with stronger results for homogeneous knots. For knots of nine or fewer …
Tutte Polynomial In Knot Theory, David Alan Petersen
Tutte Polynomial In Knot Theory, David Alan Petersen
Theses Digitization Project
This thesis reviews the history of knot theory with an emphasis on the diagrammatic approach to studying knots. Also covered are the basic concepts and notions of graph theory and how these two fields are related with an example of a knot diagram and how to associate it to a graph.
An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins
An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins
Theses Digitization Project
This thesis covers improvements on the upperbounds for ropelength of a specific class of algebraic knots.
Virtual Spatial Graphs, Thomas Fleming, Blake Mellor
Virtual Spatial Graphs, Thomas Fleming, Blake Mellor
Mathematics Faculty Works
Two natural generalizations of knot theory are t he study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin the study of virtual spat ial graphs.