› Electronic Theses and Dissertations

# Crossing Number Bounds of Mosaic Knot Diagrams

## Electronic Theses and Dissertations

### Item Details

abstract
In this thesis, we tabulate some previously undocumented link mosaic diagrams. Next we prove an upper and lower bound on crossing number of certain mosaic diagrams of knots in terms of winding number for knot diagrams that make only counterclockwise turns. Next we begin drawing mosaic diagrams that have a more grid-like structure and no crossings. This grid structure of a knot is similar to a grid diagram" which is equivalent to the arc presentation of a knot diagram. We generate grid diagrams using pairs of permutations from the group $((S_{n-1}\times S_n)$. These permutations form a set of coordinate pairs that locate the position of a turn tile in the diagram.
subject
arc presentation
bounds
grid diagram
knot
mosaic
contributor
Parsley, Robert J (committee chair)
Howards, Hugh N (committee member)
Rouse, Jeremy A (committee member)
date
2017-06-15T08:36:13Z (accessioned)
2017-06-15T08:36:13Z (available)
2017 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/82244 (uri)
language
en (iso)
publisher
Wake Forest University
title
Crossing Number Bounds of Mosaic Knot Diagrams
type
Thesis