POLYATOR — POLYA POLYNOMIAL COMPUTATION IN YOUR BROWSER
OPEN THE APP
Enter the names of the positions, the generating permutations, and the number of colors.
Enter positions and permutations as strings separated by spaces and/or commas. Enter each generating permutation as a rearrangement of the positions.
Then click GO.
Suppose we want to model a three-by-three grid of cells. We arbitrarily name these a through i, arranged like so:
a b c
d e f
g h i
We enter this as a,b,c,d,e,f,g,h,i in the first field.
Let's say our allowable operations are to rotate and flip this grid. Two permutations can generate this entire group. Let us pick one rotation
c f i
b e h
a d g
which we will enter as c,f,i,b,e,h,a,d,g in the second field, and one reflection
c b a
f e d
i h g
which we will enter as c,b,a,f,e,d,i,h,g on a second line in the second field.
Finally, we enter a number of colors in the third field. When GO is pressed, a table with two columns is displayed: the left column shows a particular breakdown of how many of each color is used, and the right column shows how many different ways this can be done, under the group of permutations we've specified.