FIGURES.md

Reproducing the Figures

Below we list the figures in the paper that deal with timing experiments and include details on how to generate the data for each one.

Figure 5: Algorithm Scaling with Colors

We used a transitive group constructed from $S_3\times S_4$ (thus with 144 group elements). This group is stored in the file fortran/tests/group.out.cr1. Additionally, the generators are contained in the same folder in a file generators.in.cr1.

Colors	Stochiometry
2	10 10
3	10 5 5
4	5 5 5 5
5	4 4 4 4 4
6	4 4 4 4 2 2
7	4 4 4 2 2 2 2
8	4 4 2 2 2 2 2 2
9	4 2 2 2 2 2 2 2 2
10	2 2 2 2 2 2 2 2 2 2

The Polya value for the first entry in the table can be generated using ./polya.out 10 10 -group group.out.cr1.

Figure 6: Algorithm Scaling with Number of Elements in the Set

For a fixed color selection (only 2 colors), we adjust the stoichiometry as follows:

Group	Stochiometry
fg1	6 6
fg2	9 9
fg3	10 10
fg4	12 12
fg5	15 15
fg6	20 20
fg7	55 17
fg8	110 10

The groups are located at fortran/tests/, with files labeled group.out.{group}, with {group} being one of the fg* in the table above. The groups are all isomorphic to $S_3\times S_4$ (thus with 144 group elements), but constructed carefully to be transitive on the sites. Additionally, the generators are contained in the same folder in a file generators.in.fg*.

The Polya value for the first entry in the table can be generated using ./polya.out 6 6 -group group.out.fg1.

Figure 7: Algorithm Scaling with Group Size

We used the unique permutation groups arising from all derivative super structures of a simple cubic lattice for a given number of sites in the unit cell. The groups can be found in the group.out.sc* files in fortran/tests/. Additionally, the generators are contained in the same folder in a file generators.in.sc_*.

Group	Stochiometry
sc_16*	8 8
sc_24*	12 12
sc_32*	16 16
sc_48*	24 24
sc_60*	30 30