Built-in Mathematica Symbol

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, {n_min, n_max}]
gives all subsets containing between n_min and n_max elements.

Subsets[list, nspec, s]
limits the result to the first s subsets.

Subsets[list, nspec, {s}]
gives if possible the s

subset.

MORE INFORMATION

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, {n_min, n_max, dn}] gives subsets containing n_min, n_min+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

CLOSE ALL

Basic Examples (2)

All possible subsets (power set):

All possible subsets containing up to 2 elements:

Subsets containing exactly 2 elements:

All possible subsets (power set):

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All possible subsets containing up to 2 elements:

In[1]:=

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Subsets containing exactly 2 elements:

In[2]:=

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Scope (4)

The first 5 subsets containing 3 elements:

All subsets with even length:

The 69381

subset:

All subsets of {a, b, c, d}:

The odd-numbered subsets of {a, b, c, d}, in reverse order:

Generalizations & Extensions (1)

Use any head:

Applications (7)

Find all ways to pick 3 elements from 4:

Draw lines between all pairs of points in an octagon:

Construct an elementary symmetric polynomial:

All possible subsets of the divisors of 10:

Find integers that have exactly 3 nonzero binary digits:

Join all possible pairs of 20 random points in 3D:

Draw lines between all pairs of points in a cube:

Properties & Relations (3)

Subsets picks out first the elements that appear first in the input:

Different occurrences of the same element are treated as distinct:

Tuples gives all possible combinations and reorderings of elements:

Possible Issues (1)

Subsets[a, b, c]

Take[Subsets[a, b], c] only when all requested items are present:

When items requested by c are missing, the ones present are returned:

To suppress the warning message, use Off:

Neat Examples (2)

Polygons formed from all possible triples of random points: