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I am a mathematics major from Virginia Beach, Virginia with the goal of becoming a research mathematician. Currently, my academic interests are in algebra and artificial intelligence. In my free time I enjoy listening to music, hiking, and hanging out with my friends. You can find more information about me on my website (<a href="https://iannbridges.com"> click here!</a>)

Tilings of Three Dimensional Deficient Rectangles with L-Tetrominoes

Abstract

We consider three dimensional iterations of the L-tetrominoe. We show that three dimensional rectangles missing one square, called deficient rectangles, can be tiled as long as they satisfy two conditions: minimum side length 3, and all sides are congruent to 1 (mod 4) or two sides that are congruent to 3 (mod 4) and one side is 1 (mod 4).

Keywords: mathematics tiling proofs algebra number