Generate All Partitions of a List

The new functions FoldPair and FoldPairList allow mapping simultaneously an output function and a state-update function.

Take a length-5 list to be partitioned.

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list = {a, b, c, d, e};

Use FoldPairList together with TakeDrop to generate a partition of the following lengths.

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lengths = {2, 2, 1}; FoldPairList[TakeDrop, list, lengths]

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To construct all partitions, find all possible decompositions of the number 5.

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lengthsAll = Flatten[Permutations /@ IntegerPartitions[5], 1]

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In[4]:=

FoldPairList[TakeDrop, list, #] & /@ lengthsAll // Column

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