%0 Generic %1 group2023integer %A Group, MIT CompGeom %A Abel, Zachary %A Akitaya, Hugo A. %A Demaine, Erik D. %A Hesterberg, Adam C. %A Lynch, Jayson %D 2023 %K combinatorics computational_geometry geometry mathematics %T When Can You Tile an Integer Rectangle with Integer Squares? %U http://arxiv.org/abs/2308.15317 %X 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.

@misc{group2023integer, abstract = {This paper characterizes when an $m \times n$ 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.}, added-at = {2023-09-03T00:20:34.000+0200}, author = {Group, MIT CompGeom and Abel, Zachary and Akitaya, Hugo A. and Demaine, Erik D. and Hesterberg, Adam C. and Lynch, Jayson}, biburl = {https://www.bibsonomy.org/bibtex/23cb3fb01c40d601fecf0e050457fa611/tabularii}, description = {When Can You Tile an Integer Rectangle with Integer Squares?}, interhash = {41d701a785f007e90bcf753ce8aa3af0}, intrahash = {3cb3fb01c40d601fecf0e050457fa611}, keywords = {combinatorics computational_geometry geometry mathematics}, note = {cite arxiv:2308.15317Comment: 6 pages, 1 figure}, timestamp = {2023-09-03T00:23:10.000+0200}, title = {When Can You Tile an Integer Rectangle with Integer Squares?}, url = {http://arxiv.org/abs/2308.15317}, year = 2023 }