MATHEMATICS COLLOQUIUM
Speaker: Claus Ernst.
Title:
The Complexity of Knots and Links on the Cubic Lattice.
Affiliation: Western Kentucky University.
Date: Friday, November 30, 2001.
Place and Time: Room 101 - Love Building, 3:35-4:35 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.
Abstract.
The cubic lattice is the graph in R^3 whose vertices consist of
all points with integer coordinates and whose edges consist of line
segments of unit length connecting these vertices. A lattice polygon
(knot) is a simple
closed curve on the cubic lattice and a lattice link consists of
several disjoint lattice polygons.
In this talk I will concentrate on the relationship between the
length of the lattice knot or link and the number of crossings in a
diagram. Large examples of knot and links on the cubic lattice will
be presented that give us some insight in how many crossing on can
generated using n steps in a lattice polygon.
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