19th Annual Student Research Conference
Mathematics and Computer Science
On the Generation and Frequency of Sturmian and One-Dimensional Cut and Project Sequences
Kensey L. Riley
Dr. David Garth, Faculty Mentor
We looked at Sturmian words and one-dimensional cut and project sequences. A Sturmian word is one for which the number of factors of length n is n + 1. The cut and project method is given by taking a line y =αx of irrational slope and a strip parallel to the line, and then projecting the points of the integer lattice in the strip orthogonally onto the line. This tiles the line into infinitely many line segments. Labeling these line segments with characters from a finite alphabet creates the cut and project word. Recently it was shown that binary cut and project words are Sturmian. We will show some properties of Sturmian words using the cut and project method.
Keywords: cut and project , sturmian words
Topic(s):Mathematics
Presentation Type: Oral Paper
Session: 51-3
Location: OP 2111
Time: 3:15