Publication Date


Document Type


Committee Members

David Miller (Committee Member), Steen Pedersen (Committee Chair), Jim Vance (Committee Member)

Degree Name

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.

Page Count


Department or Program

Department of Mathematics and Statistics

Year Degree Awarded