I know there's a way to split a list into parts of a specific length, and I know there's a way to get all possible partitions of an integer. But I was wondering if there's a way to partition a list into, say, three parts. Kind of like the balls and dividers method, except that it actually returns the number of balls between each set of dividers. So if I put in something like:
f[4,2] or f[{1,1,1,1},2] it will return
{2,2},{1,3},{3,1} or {{1,1},{1,1}},{{1},{1,1,1}},{{1,1,1},{1}} 
ClearAll[f]; f[n_Integer, m_Integer] := DeleteDuplicates[Join@@Permutations/@IntegerPartitions[n, {m}]] f[x_List, m_Integer] := Module[{n=Length@x}, Internal`PartitionRagged[x, #] & /@ f[n, m]] Examples:
f[4, 2] {{3, 1}, {2, 2}, {1, 3}}
f[{1, 1, 1, 1}, 2] {{{1, 1, 1}, {1}},
{{1, 1}, {1, 1}},
{{1}, {1, 1, 1}}}
f[5, 3] {{3, 1, 1}, {1, 3, 1}, {1, 1, 3}, {2, 2, 1}, {2, 1, 2}, {1, 2, 2}}
f[Range@5, 3] {{{1, 2, 3}, {4}, {5}},
{{1}, {2, 3, 4}, {5}},
{{1}, {2}, {3, 4, 5}},
{{1, 2}, {3, 4}, {5}},
{{1, 2}, {3}, {4, 5}},
{{1}, {2, 3}, {4, 5}}}
FrobeniusSolve[] instead: f[n_Integer, m_Integer] := Select[FrobeniusSolve[ConstantArray[1, m], n], FreeQ[0]] $\endgroup$ For partitioning a list, you can use the Basic Example from the Help page for ReplaceList. For example,
ReplaceList[{1, 1, 1, 1}, {x__, y__} -> {{x}, {y}}] or
ReplaceList[Range[5], {x__, y__, z__} -> {{x}, {y}, {z}}] 