Function Repository Resource:

OrderlessCombinations

Source Notebook

Generate all possible orderless lists of a given length with a given set of elements

Contributed by: Jon McLoone

ResourceFunction["OrderlessCombinations"][list,n]

gives all possible orderless sets comprised of the elements of list up to length n.

ResourceFunction["OrderlessCombinations"][list,{n}]

gives sets of exactly length n.

ResourceFunction["OrderlessCombinations"][list,{n,m}]

gives sets containing between n and m elements.

Examples

Basic Examples (2)

There are nine possible orderless sets of up to two elements chosen from three possible elements:

In[1]:=

Out[1]=

There are six possible orderless sets of exactly two elements chosen from three possible elements:

In[2]:=

Out[2]=

Scope (2)

Get length four sets from a list of length two:

In[3]:=

Out[3]=

Elements need not be integers:

In[4]:=

Out[4]=

Applications (1)

A company makes three different heating units. The customer needs a row of five heating units for a large room. How many different purchase combinations are available to the customer:

In[5]:=

Out[5]=

Properties and Relations (1)

The same sets can be generated by sorting and deduplicating the output of Tuples, but OrderlessCombinations is faster, and uses much less memory for larger problems:

In[6]:=