Tilings in the 3 dimensional lattice with L-tetrominoes

Authors

Ian N. Bridges, Florida State UniversityFollow

Abstract

We consider three dimensional L-tetrominoes. We show that there exists at least one way to tile every three dimensional rectangle whose side lengths are at least $3$ and area is congruent to $1 \pmod 4$ such that one square goes untiled. In addition, we show that every three dimensional rectangle is tileable provided one side has length at least $2$ and the other is a multiple of $4$.

Author Bio

Ian Bridges is a mathematics student at Florida State University with plans to pursue his Ph.D. in the field of dynamical systems. He currently works as a research assistant in the field of quantum error correction.

Faculty Sponsor

Cynthia Lester

Recommended Citation

Bridges, Ian N. (2025) "Tilings in the 3 dimensional lattice with L-tetrominoes," Rose-Hulman Undergraduate Mathematics Journal: Vol. 26: Iss. 1, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol26/iss1/1