Tiling Rectangles and 2-Deficient Rectangles with L-Pentominoes

Authors

Monica Kane, California Lutheran UniversityFollow

Abstract

We investigate tiling rectangles and 2-deficient rectangles with L-pentominoes. First, we determine exactly when a rectangle can be tiled with L-pentominoes. We then determine locations for pairs of unit squares that can always be removed from an m × n rectangle to produce a tileable 2-deficient rectangle when m ≡ 1 (mod 5), n ≡ 2 (mod 5) and when m ≡ 3 (mod 5), n ≡ 4 (mod 5).

Author Bio

Monica Kane graduated in 2019 with a B.S. in mathematics from California Lutheran University, where she completed this research during her senior year. She is currently working as a software developer.

Faculty Sponsor

Michael Gagliardo

Recommended Citation

Kane, Monica (2022) "Tiling Rectangles and 2-Deficient Rectangles with L-Pentominoes," Rose-Hulman Undergraduate Mathematics Journal: Vol. 23: Iss. 1, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol23/iss1/6