dear Erik,

> Does the number include symmetrical positions (rotations / mirroring / color
> reversal)?

Yes, of course.
This is also apparent from the table at the bottom listing 57 legal
2x2 positions. Figure 4 on page 5 of our paper
  http://tromp.github.io/go/gostate.pdf
shows how these 57 positions form 13 equivalence classes with respect
to mirroring/reflection which further reduces to 7 classes when
considering color symmetry as well.

regards,
-John
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