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EXAMPLE
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The totally symmetric solid partitions up to n=15 are:
[{{1}}]
[{{2,1}, {1}}, {{1}}]
[{{3,1,1}, {1}, {1}}, {{1}}, {{1}}]
[{{2,2}, {2,1}}, {{2,1}, {1}}]
[{{4,1,1,1}, {1}, {1}, {1}}, {{1}}, {{1}}, {{1}}]
[{{3,2,1}, {2,1}, {1}}, {{2,1}, {1}}, {{1}}] and
[{{2,2}, {2,2}}, {{2,2}, {2,1}}]
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