Hot answers tagged partitions
James Stirling has the wisdom. A Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of $n$ objects into $k$ non-empty subsets. In this case, we multiply by $k!$ since we have labeled subsets. So the number is $$4!\ S(9,4)=186480.$$
In order to see the "correct" behavior of the Schur polynomials and to be able to compare different formulas for the Schur polynomials, the number of variables you need is equal to the total number of boxes in the partition (the value $d$, in the Wikipedia notation), not just the number of (nonzero) parts in the partition. Try taking $n=d=4$ in both of your ...
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