#### Submission Title

Tilings of Modified Rectangles by Ribbon-Tile Pentominoes

#### Faculty Sponsor(s)

Michael Hitchman

#### Subject Area

Mathematics

#### Description

Which dimensions of *a* and *b* satisfy tilings of modified rectangles by ribbon tile pentominoes? We answer this question using tile invariants developed in prior research on the mathematics of tiling, as well as the use of inductive lemmas. The set of tiles we use for this study are height-1 ribbon tile pentominoes, which we later define. Modified rectangles are *a*-by-*b* rectangles with height *a* and width *b*, and the additional feature that the top left and bottom right squares are removed.

#### Recommended Citation

Thompson, Elizabeth, "Tilings of Modified Rectangles by Ribbon-Tile Pentominoes" (2021). *Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement.* Event. Submission 9.

https://digitalcommons.linfield.edu/symposium/2021/all/9

Tilings of Modified Rectangles by Ribbon-Tile Pentominoes

Which dimensions of *a* and *b* satisfy tilings of modified rectangles by ribbon tile pentominoes? We answer this question using tile invariants developed in prior research on the mathematics of tiling, as well as the use of inductive lemmas. The set of tiles we use for this study are height-1 ribbon tile pentominoes, which we later define. Modified rectangles are *a*-by-*b* rectangles with height *a* and width *b*, and the additional feature that the top left and bottom right squares are removed.