David Miller (Committee Member), Steen Pedersen (Committee Chair), Jim Vance (Committee Member)
Master of Science (MS)
We define a family of deleted digits Cantor sets which satisfy specific constraints on the generating set of digits. We explore the structure and dimension of the intersection of a deleted digits Cantor set with its translate by a real value t. These results apply directly to the traditional Middle Thirds Cantor set as well as regular and uniform Cantor sets. We show that this family includes certain irregular sets which have not been previously analyzed. Our methods not only reveal the upper and lower bounds for the Minkowski dimension, but also uncover a formula for calculating the dimension of these intersections when specific conditions are met.
Department or Program
Department of Mathematics and Statistics
Year Degree Awarded
Copyright 2011, all rights reserved. This open access ETD is published by Wright State University and OhioLINK.