Arts and Sciences
Mathematics and Computer Science
A de Bruijn Array (also called a torus) is a toroidal array of numbers where each filling of an m-by-n matrix, with digits chosen from 0 to k-1, is present only once. While it is well understood how to find a de Bruijn Array for fillings of an m-by-m rectangle (Jackson, Stevens, Hurlbert, 2009), arrays for other shapes are unstudied. I have worked to answer the question: can de Bruijn Arrays be found with different shapes of fillings? In particular, I have considered The L Problem. Instead of arranging fillings of a rectangular grid, this problem arranges fillings of a 2-by-2 grid with one square removed. I have proven that a de Bruijn Array does exist for every alphabet using this pattern.
Rockey, Rachel, "Compactly Arranging Every Way of Filling an L-Shaped Grid into a Non-Repeating Array" (2014). Symposium on Undergraduate Research and Creative Expression (SOURCE). 352.