This is the repository for Zach's enumerator of grid graph partitions. For details about the algorithm and an implementation, see the Jupyter notebook.

The enumerations folder contains .zips of the enumerations of the valid partitions. Each zip contains a single text file. The data format is as follows. Each partition is on its own line. Reading off the grid left-to-right, top-to-bottom, a partition appears as a comma-delimited list where each value corresponds to the chunk to which that cell belongs. For example, the partition

1 1 2  
1 2 2  
3 3 3

is represented as 1,1,2,1,2,2,3,3,3.

The file naming convention is [<m>,<n>]_[<p_1>,<p_2>,...,<p_l>]_k_<cont>.zip where m and n are the dimensions of the grid, the p_i are the allowed sizes of the chunks, k is the number of pieces, and cont is either rc for rook contiguity or qc for queen contiguity. The .zip contains a .txt file of the same name.

The table is a reference which contains the sizes of some of the various sets of enumerations.

This is Julia code. If you already have Julia and Jupyter installed, you can set up IJulia by calling Pkg.add("IJulia") in the Julia REPL. If you don't have either of these set up, you can get Julia from the creators at julialang.org and Jupyter from jupyter.org.

Coming soon: a command line version of this tool