This is the list of F curves up to $S_n$ symmetry, i.e., this function generates partitions of the integer $n$ into 4 positive integers, not partitions of the set {1,...,n} into four nonempty subsets.
i1 : symmetricFCurves(8)
o1 = {{5, 1, 1, 1}, {4, 2, 1, 1}, {3, 3, 1, 1}, {3, 2, 2, 1}, {2, 2, 2, 2}}
o1 : List
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The object symmetricFCurves is a method function.