X would seem to be a lot more simply encoded as a single index. whether the one immediately before the cut or immediately after doesn't really matter, your pairs in X will always be consecutive (with wrapping) I assume.
also, if you could then encode Y as just an ordering of the parts from X rather than the components therein that would be a lot easier. i.e. Y would just be a permutation whose length is equal to the number of sections you end up with from your cuts in X. In a general case this would usually be numel(X) + 1, though in the specific example you give it is just numel(X) as an edge case.
