--- title: "Rearranging & Restructuring Lists" language: "en" type: "Guide" summary: "The Wolfram Language encapsulates in a small number of functions vast flexibility in rearranging lists with any structure and any number of elements." sections: - title: "Sequence-Oriented Operations" link: "null" - title: "Element-Oriented Operations" link: "paclet:guide/ElementsOfLists" keywords: - absent from list - alphabetic - alphabetizing of lists - append to - appending - arrange - array flatten - ascending order - Beck parameters - block matrices - blocking lists - blocks - canonical order - catenating lists - census - changing parts - circular partitioning - collapse - collating of strings - collation - combinations - combining lists - concatenating lists - contraction - cycle - cyclic partitioning - decreasing order - deleting elements - descending order - difference of sets - discard elements - disjointness - distinct elements in lists - dithering - encoding - equivalence class counting - extraction of sublists - flat list - flatten at - flatten matrix - frequencies - gather - gathering elements in lists - generating tuples - grade in APL - handles - hot spots - increasing order - interleave - join block matrices - join lists - knobs - k-subsets - left shift - levels - list append - list complement - lists - lists ordering - matrix transpose - merging lists - multiple parts - multiplicities - neighborhoods - one-dimensional list - ordered pairs - overhangs - overlap between lists - padding - pad left - pad right - pairs - partitioning lists - parts - perm - permutation of indices - permutations of lists - permute - picking out sequences of elements in lists - powerset - random permutation - random sample - random subset - ravel in APL - rearrangements - remove duplicates - removing elements from lists - removing sublists - reordering of lists - reorderings - replace part - replacements - reshape in APL - right shift - rotate left - rotate right - run-length encoding - run length encoding - runs of arguments - sampling without replacement - segments of lists - selecting objects with ordering - sequence of elements - set exponential - sets - sorting of lists - splicing - splitting lists - squash - stride - subexpressions - sublists - submatrices - subset permutations - subtraction of sets - tally - transpose of matrices - transposition of lists - triples - unflatten - union of sets - uniq - unique elements in lists - unravel - vectors - wraparound partitioning canonical_url: "https://reference.wolfram.com/language/guide/RearrangingAndRestructuringLists.html" source: "Wolfram Language Documentation" related_guides: - title: "List Manipulation" link: "https://reference.wolfram.com/language/guide/ListManipulation.en.md" - title: "Elements of Lists" link: "https://reference.wolfram.com/language/guide/ElementsOfLists.en.md" - title: "Applying Functions to Lists" link: "https://reference.wolfram.com/language/guide/ApplyingFunctionsToLists.en.md" - title: "Discrete Mathematics" link: "https://reference.wolfram.com/language/guide/DiscreteMathematics.en.md" - title: "Sequence Alignment & Comparison" link: "https://reference.wolfram.com/language/guide/SequenceAlignmentAndComparison.en.md" - title: "Manipulating Structured Datasets" link: "https://reference.wolfram.com/language/guide/ComputationWithStructuredDatasets.en.md" - title: "Associations" link: "https://reference.wolfram.com/language/guide/Associations.en.md" related_functions: - title: "AlphabeticSort" link: "https://reference.wolfram.com/language/ref/AlphabeticSort.en.md" - title: "Append" link: "https://reference.wolfram.com/language/ref/Append.en.md" - title: "AppendTo" link: "https://reference.wolfram.com/language/ref/AppendTo.en.md" - title: "ArrayFilter" link: "https://reference.wolfram.com/language/ref/ArrayFilter.en.md" - title: "ArrayFlatten" link: "https://reference.wolfram.com/language/ref/ArrayFlatten.en.md" - title: "ArrayPad" link: "https://reference.wolfram.com/language/ref/ArrayPad.en.md" - title: "ArrayReduce" link: "https://reference.wolfram.com/language/ref/ArrayReduce.en.md" - title: "ArrayResample" link: "https://reference.wolfram.com/language/ref/ArrayResample.en.md" - title: "ArrayReshape" link: "https://reference.wolfram.com/language/ref/ArrayReshape.en.md" - title: "Catenate" link: "https://reference.wolfram.com/language/ref/Catenate.en.md" - title: "Complement" link: "https://reference.wolfram.com/language/ref/Complement.en.md" - title: "DeleteAdjacentDuplicates" link: "https://reference.wolfram.com/language/ref/DeleteAdjacentDuplicates.en.md" - title: "DeleteDuplicates" link: "https://reference.wolfram.com/language/ref/DeleteDuplicates.en.md" - title: "DeleteDuplicatesBy" link: "https://reference.wolfram.com/language/ref/DeleteDuplicatesBy.en.md" - title: "Drop" link: "https://reference.wolfram.com/language/ref/Drop.en.md" - title: "Flatten" link: "https://reference.wolfram.com/language/ref/Flatten.en.md" - title: "FlattenAt" link: "https://reference.wolfram.com/language/ref/FlattenAt.en.md" - title: "Gather" link: "https://reference.wolfram.com/language/ref/Gather.en.md" - title: "GatherBy" link: "https://reference.wolfram.com/language/ref/GatherBy.en.md" - title: "Groupings" link: "https://reference.wolfram.com/language/ref/Groupings.en.md" - title: "Intersection" link: "https://reference.wolfram.com/language/ref/Intersection.en.md" - title: "Join" link: "https://reference.wolfram.com/language/ref/Join.en.md" - title: "LexicographicSort" link: "https://reference.wolfram.com/language/ref/LexicographicSort.en.md" - title: "Nothing" link: "https://reference.wolfram.com/language/ref/Nothing.en.md" - title: "NumericalSort" link: "https://reference.wolfram.com/language/ref/NumericalSort.en.md" - title: "PadLeft" link: "https://reference.wolfram.com/language/ref/PadLeft.en.md" - title: "PadRight" link: "https://reference.wolfram.com/language/ref/PadRight.en.md" - title: "Partition" link: "https://reference.wolfram.com/language/ref/Partition.en.md" - title: "Permutations" link: "https://reference.wolfram.com/language/ref/Permutations.en.md" - title: "RandomSample" link: "https://reference.wolfram.com/language/ref/RandomSample.en.md" - title: "ReplacePart" link: "https://reference.wolfram.com/language/ref/ReplacePart.en.md" - title: "Reverse" link: "https://reference.wolfram.com/language/ref/Reverse.en.md" - title: "ReverseSort" link: "https://reference.wolfram.com/language/ref/ReverseSort.en.md" - title: "ReverseSortBy" link: "https://reference.wolfram.com/language/ref/ReverseSortBy.en.md" - title: "Riffle" link: "https://reference.wolfram.com/language/ref/Riffle.en.md" - title: "RotateLeft" link: "https://reference.wolfram.com/language/ref/RotateLeft.en.md" - title: "RotateRight" link: "https://reference.wolfram.com/language/ref/RotateRight.en.md" - title: "SequenceReplace" link: "https://reference.wolfram.com/language/ref/SequenceReplace.en.md" - title: "SequenceSplit" link: "https://reference.wolfram.com/language/ref/SequenceSplit.en.md" - title: "Sort" link: "https://reference.wolfram.com/language/ref/Sort.en.md" - title: "SortBy" link: "https://reference.wolfram.com/language/ref/SortBy.en.md" - title: "Splice" link: "https://reference.wolfram.com/language/ref/Splice.en.md" - title: "Split" link: "https://reference.wolfram.com/language/ref/Split.en.md" - title: "SplitBy" link: "https://reference.wolfram.com/language/ref/SplitBy.en.md" - title: "Subsequences" link: "https://reference.wolfram.com/language/ref/Subsequences.en.md" - title: "Subsets" link: "https://reference.wolfram.com/language/ref/Subsets.en.md" - title: "Take" link: "https://reference.wolfram.com/language/ref/Take.en.md" - title: "TakeList" link: "https://reference.wolfram.com/language/ref/TakeList.en.md" - title: "Tally" link: "https://reference.wolfram.com/language/ref/Tally.en.md" - title: "Transpose" link: "https://reference.wolfram.com/language/ref/Transpose.en.md" - title: "Tuples" link: "https://reference.wolfram.com/language/ref/Tuples.en.md" - title: "Union" link: "https://reference.wolfram.com/language/ref/Union.en.md" related_tutorials: - title: "Lists as Sets" link: "https://reference.wolfram.com/language/tutorial/Lists.en.md#20366" - title: "Rearranging Lists" link: "https://reference.wolfram.com/language/tutorial/Lists.en.md#1331" - title: "Rearranging Nested Lists" link: "https://reference.wolfram.com/language/tutorial/Lists.en.md#7768" - title: "Partitioning and Padding Lists" link: "https://reference.wolfram.com/language/tutorial/ManipulatingLists.en.md#14460" - title: "Grouping and Combining Elements of Lists" link: "https://reference.wolfram.com/language/tutorial/Lists.en.md#16859" - title: "Ordering in Lists" link: "https://reference.wolfram.com/language/tutorial/Lists.en.md#6191" - title: "Combining Lists" link: "https://reference.wolfram.com/language/tutorial/Lists.en.md#41" --- # Rearranging & Restructuring Lists The Wolfram Language encapsulates in a small number of functions vast flexibility in rearranging lists with any structure and any number of elements. --- [`Flatten`](https://reference.wolfram.com/language/ref/Flatten.en.md) — flatten out any sequence of levels in a nested list [`Partition`](https://reference.wolfram.com/language/ref/Partition.en.md) — partition lists or nested lists into sublists [`Join`](https://reference.wolfram.com/language/ref/Join.en.md) — join lists together at any level [`Catenate`](https://reference.wolfram.com/language/ref/Catenate.en.md) — catenate elements from a list of lists * [`ArrayFlatten`](https://reference.wolfram.com/language/ref/ArrayFlatten.en.md) * [`ArrayReshape`](https://reference.wolfram.com/language/ref/ArrayReshape.en.md) * [`FlattenAt`](https://reference.wolfram.com/language/ref/FlattenAt.en.md) * [`Splice`](https://reference.wolfram.com/language/ref/Splice.en.md) * [`Nothing`](https://reference.wolfram.com/language/ref/Nothing.en.md) [`TakeList`](https://reference.wolfram.com/language/ref/TakeList.en.md) — take a succession of sublists from a list --- [`Sort`](https://reference.wolfram.com/language/ref/Sort.en.md) — sort lexicographically or with any comparison function [`ReverseSort`](https://reference.wolfram.com/language/ref/ReverseSort.en.md) — sort reverse lexicographically [`SortBy`](https://reference.wolfram.com/language/ref/SortBy.en.md) — sort by the values of a function applied to elements * [`AlphabeticSort`](https://reference.wolfram.com/language/ref/AlphabeticSort.en.md) * [`NumericalSort`](https://reference.wolfram.com/language/ref/NumericalSort.en.md) * [`LexicographicSort`](https://reference.wolfram.com/language/ref/LexicographicSort.en.md) * [`ReverseSortBy`](https://reference.wolfram.com/language/ref/ReverseSortBy.en.md) [`Reverse`](https://reference.wolfram.com/language/ref/Reverse.en.md) — reverse a list at any level [`RotateLeft`](https://reference.wolfram.com/language/ref/RotateLeft.en.md), [`RotateRight`](https://reference.wolfram.com/language/ref/RotateRight.en.md) — cyclically rotate lists at any depth --- [`Transpose`](https://reference.wolfram.com/language/ref/Transpose.en.md) — transpose any collection of levels [`ArrayReduce`](https://reference.wolfram.com/language/ref/ArrayReduce.en.md) — reduce dimensions of an array by applying a function --- [`ArrayResample`](https://reference.wolfram.com/language/ref/ArrayResample.en.md) — resample an array to higher or lower resolution [`ArrayPad`](https://reference.wolfram.com/language/ref/ArrayPad.en.md) — add padding on each side [`ArrayFilter`](https://reference.wolfram.com/language/ref/ArrayFilter.en.md) — filter an array using local neighborhoods [`Riffle`](https://reference.wolfram.com/language/ref/Riffle.en.md) — intersperse additional elements [`PadLeft`](https://reference.wolfram.com/language/ref/PadLeft.en.md), [`PadRight`](https://reference.wolfram.com/language/ref/PadRight.en.md) — pad lists to be a particular length at any depth --- [`Split`](https://reference.wolfram.com/language/ref/Split.en.md) — split into runs of identical elements [`Gather`](https://reference.wolfram.com/language/ref/Gather.en.md) — gather sublists of identical elements [`Union`](https://reference.wolfram.com/language/ref/Union.en.md), [`Tally`](https://reference.wolfram.com/language/ref/Tally.en.md) — enumerate, tally all distinct elements in a list [`DeleteDuplicates`](https://reference.wolfram.com/language/ref/DeleteDuplicates.en.md) — delete duplicate elements in a list [`DeleteDuplicatesBy`](https://reference.wolfram.com/language/ref/DeleteDuplicatesBy.en.md) — delete elements for which values of a function are duplicated [`DeleteAdjacentDuplicates`](https://reference.wolfram.com/language/ref/DeleteAdjacentDuplicates.en.md) — delete duplicates adjacent to one another [`SplitBy`](https://reference.wolfram.com/language/ref/SplitBy.en.md), [`GatherBy`](https://reference.wolfram.com/language/ref/GatherBy.en.md) — split, gather based on values of a function applied to elements * [`Tuples`](https://reference.wolfram.com/language/ref/Tuples.en.md) * [`Subsets`](https://reference.wolfram.com/language/ref/Subsets.en.md) * [`Subsequences`](https://reference.wolfram.com/language/ref/Subsequences.en.md) * [`Permutations`](https://reference.wolfram.com/language/ref/Permutations.en.md) * [`RandomSample`](https://reference.wolfram.com/language/ref/RandomSample.en.md) [`Groupings`](https://reference.wolfram.com/language/ref/Groupings.en.md) — generate all possible groupings of a list into sublists --- * [`Union`](https://reference.wolfram.com/language/ref/Union.en.md) * [`Intersection`](https://reference.wolfram.com/language/ref/Intersection.en.md) * [`Complement`](https://reference.wolfram.com/language/ref/Complement.en.md) --- ### Sequence-Oriented Operations [`SequenceSplit`](https://reference.wolfram.com/language/ref/SequenceSplit.en.md) — split a list at sequences matching a pattern [`SequenceReplace`](https://reference.wolfram.com/language/ref/SequenceReplace.en.md) — replace sequences in a list ### [Element-Oriented Operations](https://reference.wolfram.com/language/guide/ElementsOfLists.en.md) * [`ReplacePart`](https://reference.wolfram.com/language/ref/ReplacePart.en.md) * [`Take`](https://reference.wolfram.com/language/ref/Take.en.md) * [`Drop`](https://reference.wolfram.com/language/ref/Drop.en.md) * [`Append`](https://reference.wolfram.com/language/ref/Append.en.md) * [`AppendTo`](https://reference.wolfram.com/language/ref/AppendTo.en.md) ## Tech Notes * [Lists as Sets](https://reference.wolfram.com/language/tutorial/Lists.en.md#20366) * [Rearranging Lists](https://reference.wolfram.com/language/tutorial/Lists.en.md#1331) * [Rearranging Nested Lists](https://reference.wolfram.com/language/tutorial/Lists.en.md#7768) * [Partitioning and Padding Lists](https://reference.wolfram.com/language/tutorial/ManipulatingLists.en.md#14460) * [Grouping and Combining Elements of Lists](https://reference.wolfram.com/language/tutorial/Lists.en.md#16859) * [Ordering in Lists](https://reference.wolfram.com/language/tutorial/Lists.en.md#6191) * [Combining Lists](https://reference.wolfram.com/language/tutorial/Lists.en.md#41) ## Related Guides * [List Manipulation](https://reference.wolfram.com/language/guide/ListManipulation.en.md) * [Elements of Lists](https://reference.wolfram.com/language/guide/ElementsOfLists.en.md) * [Applying Functions to Lists](https://reference.wolfram.com/language/guide/ApplyingFunctionsToLists.en.md) * [Discrete Mathematics](https://reference.wolfram.com/language/guide/DiscreteMathematics.en.md) * [Sequence Alignment & Comparison](https://reference.wolfram.com/language/guide/SequenceAlignmentAndComparison.en.md) * [Manipulating Structured Datasets](https://reference.wolfram.com/language/guide/ComputationWithStructuredDatasets.en.md) * [`Associations`](https://reference.wolfram.com/language/guide/Associations.en.md)