2023/08/29 by Zachary Abel, MIT CompGeom Group, Abel, Zachary +8
Computer Science · Materials Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2308.15317
openalex publication_date 2023/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper characterizes when an m × n rectangle, where m and n are integers, can be tiled (exactly packed) by squares where each has an integer side length of at least 2. In particular, we prove that tiling is always possible when both m and n are sufficiently large (at least 10). When one dimension m is small, the behavior is eventually periodic in n with period 1, 2, or 3. When both dimensions m,n are small, the behavior is determined computationally by an exhaustive search.