I started a new project: studying polyomino tilings and related problems (very much inspired by Golomb’s famous Polyominoes). As part of this study, I waded through many papers, trying to piece together a coherent picture of how these tilings work. How I understand them is written down in this essay:

**Contents**

- Tiling Criteria
- Flow
- The Marriage Theorem
- Cylinder Deletion
- Coloring

- The Internal Structure of Domino Tilings
- Cycles
- Frozen cells
- Tiling Transformations

Here are some pages from the essay: