Generating all $k$ combinations from $n$ objects

Question

Suppose I have $n$ numbers $\{1,2,\cdots,n\}$, is there a very quick way of generating $k$-combinations using Mathematica?

Note also that Range[n] = {1, 2, ... , n} is useful for generating the list of numbers in the first place. — thorimur, Nov 30 '22 at 02:42

bmf · Accepted Answer · 2022-11-30T06:14:58.023

3

In the answer below n=3 and k=2

Tuples[{1, 2, 3}, 2]

Compare to SubSets

Subsets[{1, 2, 3}, 2]

Edit: many thanks to @BobHanlon for suggesting:

Subsets[{1, 2, 3}, {2}]

edited Nov 30 '22 at 06:14

answered Nov 30 '22 at 00:26

bmf

4

Should probably include Subsets[{1, 2, 3}, {2}] – Bob Hanlon Nov 30 '22 at 01:55
@BobHanlon Can these subsets be generated iteratively instead of all at once? – licheng Nov 30 '22 at 08:11
1

@licheng See e.g. this question for lazy generation of subsets – Lukas Lang Nov 30 '22 at 11:41

1 Answers1