Abstract
While investigating the N-Queens Puzzle, Thomas Preußer came to a simplification for the search; this is generalized and proven here. The main point is: if you have a suitable mapping of a big set to a small one, explore and use the symmetry of the small set, and transfer the result to the big set. With this mapping and the lemma, you no longer bother with the symmetry of a single element in the big set.The paper is written for two different groups: first for computer scientists implementing searches under symmetry, and second for mathematicians supporting them, and interested in understanding how search spaces can be diminished under symmetry.
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