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Instantuse addon functions for the Wolfram Language
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Get a pair of lists representing the Ferrers diagram of a partition
ResourceFunction["FrobeniusSymbolFromPartition"][λ] gives a pair of lists that count dots in the rows and columns relative to the diagonal of the Durfee square in the Ferrers diagram of the partition λ. 
Compute the Frobenius symbol of a partition:
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Here we use a partition of 8 consisting of only one large part:
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Here the partition is 11111111, with many small parts:
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Here is an intermediate case:
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A partition is a list of nonincreasing positive integers:
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Here is its Ferrers diagram:
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Define a function to illustrate the definition of the Frobenius symbol:
The number of dots in the rows to the right of the diagonal is 6, 5, 1. The number of dots in the columns below the diagonal is 4, 2, 0:
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These lists are the rows of the Frobenius symbol of the partition:
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Here is another example:
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Confirm that Frobenius symbols and partitions round trip as expected:
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Wolfram Language 11.3 (March 2018) or above
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