Subsets[list]
gives a list of all possible subsets of list.
Subsets[list,n]
gives all subsets containing at most n elements.
Subsets[list,{n}]
gives all subsets containing exactly n elements.
Subsets[list,{nmin,nmax}]
gives all subsets containing between nmin and nmax elements.
Subsets[list,nspec,s]
limits the result to the first s subsets.
Subsets[list,nspec,{s}]
gives if possible the s
subset.
Subsets
Subsets[list]
gives a list of all possible subsets of list.
Subsets[list,n]
gives all subsets containing at most n elements.
Subsets[list,{n}]
gives all subsets containing exactly n elements.
Subsets[list,{nmin,nmax}]
gives all subsets containing between nmin and nmax elements.
Subsets[list,nspec,s]
limits the result to the first s subsets.
Subsets[list,nspec,{s}]
gives if possible the s
subset.
Details
- Subsets[list] gives the power set of list.
- Subsets[list] orders subsets with shortest first, and later elements in list omitted first.
- If the elements of list are in the order returned by Sort, then the complete result from Subsets[list] will also be in this order.
- Subsets[list,All] is equivalent to Subsets[list].
- Subsets[list,{nmin,nmax,dn}] gives subsets containing nmin, nmin+dn, … elements.
- Subsets[list,nspec,spec] gives the same result as Take[Subsets[list,nspec],spec], provided that the elements specified by spec are present.
Examples
open all close allBasic Examples (2)
Scope (4)
The first 5 subsets containing 3 elements:
Subsets[{a, b, c, d, e}, {3}, 5]Subsets[{a, b, c, d, e}, {0, 5, 2}]Subsets[Range[20], All, {69381}]Subsets[{a, b, c, d}]The odd-numbered subsets of {a,b,c,d} in reverse order:
Subsets[{a, b, c, d}, All, {15, 1, -2}]Generalizations & Extensions (1)
Applications (7)
Find all ways to pick 3 elements from 4:
Subsets[{1, 2, 3, 4}, {3}]Binomial[4, 3]Draw lines between all pairs of points in an octagon:
Graphics[Line[Subsets[Table[{Cos[2Pi i / 8], Sin[2 Pi i / 8]}, {i, 8}], {2}]]]Construct an elementary symmetric polynomial:
Total[Subsets[Times[a, b, c, d, e], {3}]]All possible subsets of the divisors of 10:
Subsets[Divisors[10]]Find integers that have exactly 3 nonzero binary digits:
Subsets[{1, 2, 4, 8, 16}, {3}]Total /@ %Join all possible pairs of 20 random points in 3D:
Graphics3D[Line /@ Subsets[RandomReal[100, {20, 3}], {2}]]Draw lines between all pairs of points in a cube:
Graphics3D[Line[Subsets[Tuples[{1, 0}, 3], {2}]]]Properties & Relations (3)
Subsets picks out first the elements that appear first in the input:
Subsets[{c, b, a}]Different occurrences of the same element are treated as distinct:
Subsets[{a, b, b, b}]Tuples gives all possible combinations and reorderings of elements:
Tuples[{a, b, c}, 2]Subsets[{a, b, c}, {2}]Possible Issues (1)
Subsets[a,b,c]===Take[Subsets[a,b],c] only when all requested items are present:
Subsets[Range[4], All, 8]Take[Subsets[Range[4], All], 8]When items requested by c are missing, the ones present are returned:
Subsets[Range[3], All, 10]To suppress the warning message, use Off:
Off[Subsets::take]Subsets[Range[3], All, 10]Neat Examples (2)
Polygons formed from all possible triples of random points:
Graphics[{Opacity[0.01], Polygon /@ Subsets[RandomInteger[100, {20, 2}], {3}]}]Graphics3D[{Opacity[.1], Polygon /@ Subsets[RandomInteger[100, {10, 3}], {3}]}]Draw all possible 3D triangular polygons that can be formed with points of coordinates
, 0 or 1:
Graphics3D[Polygon[Subsets[Tuples[{-1, 0, 1}, 3], {3}]]]Tech Notes
History
Introduced in 2004 (5.1)
Text
Wolfram Research (2004), Subsets, Wolfram Language function, https://reference.wolfram.com/language/ref/Subsets.html.
CMS
Wolfram Language. 2004. "Subsets." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Subsets.html.
APA
Wolfram Language. (2004). Subsets. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Subsets.html
BibTeX
@misc{reference.wolfram_2026_subsets, author="Wolfram Research", title="{Subsets}", year="2004", howpublished="\url{https://reference.wolfram.com/language/ref/Subsets.html}", note=[Accessed: 13-June-2026]}
BibLaTeX
@online{reference.wolfram_2026_subsets, organization={Wolfram Research}, title={Subsets}, year={2004}, url={https://reference.wolfram.com/language/ref/Subsets.html}, note=[Accessed: 13-June-2026]}