Many mathematical chess problems lead to questions of the form "in how many ways can one get from position X to position Y in n moves?" Normally, either X is the Game Array, or Y must be deduced by the solver.
A common convention is that solutions differ only in the *order* in which a fixed set of moves is applied. But this is not universal, especially for "numerological" problems where the composer wants to fix a particular number (year, anniversary age, etc...)
See N. D. Elkies, New Directions in Enumerative Chess Problems, The Electronic Journal of Combinatorics, vol. 11(2), 2004.