A Computerized Search for Integral Unilateral and Equitransitive Tilings by Squares of $n$ Sizes

Rachel Jane Villafranca

Co-Presenters: Individual Presentation

College: The Dorothy and George Hennings College of Science, Mathematics and Technology

Major: Mathematical Sciences

Faculty Research Mentor: Casey Mann

Abstract:

This poster explains an algorithm that generates the possible unilateral and equitransitive tilings of the plane by squares of consecutive integer sizes, for $n ge 3$ As a preliminary result, this search discovered 3 new unilateral and equitransitive tilings by squares of 4 consecutive integer sizes that were missed by previous searches. In this poster we describe the algorithm and summarize the results so far. This was joint work done in Summer 2024 at the University of Washington Bothell mathematics REU site.