Serg wrote:53,666,689 PF-different SudokuP solution grids is the number of essentially different SudokuP solution grids.
We agree 100%!
And blue (bless his knickers) has produced a Canonical Form function that can be used to compare grids for P-equivalence and/or PF-equivalence.
The VPT group (S-equivalence) was not entirely a wasted exercise, however. blue's CF code only became available a day or two ago. Since I had already built my catalog of S-equivalence classes for SudokuP, I was able to verify that my orbit-connecting logic was correct by comparing results with CF function. So at the very least we have a reliable mechanism for orbit-connection should the need ever arise. Ok, that's probably unlikely, but we have learned much from the process. So no harm done!
And, by the way, your analysis above looks pretty fine to me in all respects. If the facts change, we simply need to change our minds (it happens to me on a regular basis!
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