Re: Combinatorics question
- Subject: [mg3309] Re: Combinatorics question
- From: ianc (Ian Collier)
- Date: 25 Feb 1996 14:28:14 -0600
- Approved: usenet@wri.com
- Distribution: local
- Newsgroups: wri.mathgroup
- Organization: Wolfram Research, Inc.
- Sender: daemon at wri.com
In article <4gi621$jkv at dragonfly.wolfram.com>, <PESCC at CUNYVM.CUNY.EDU> wrote:
> Can somenone help me find the following:
>
> I have a list of 20 numbers, and I would like to list all the
> combinations of these numbers taken 6 at a time. The Binomial
> function tells me there are 38760, but I would like to actually
> see all of them.
> Thanks in advance for your help.
You can use the KSubsets function which is defined in
DiscreteMath`Combinatorica` one of the standard packages
distributed with Mathematica.
Here is a, slightly smaller, example:
In[1]:=
nums = Range[ 6 ]
Out[1]=
{1, 2, 3, 4, 5, 6}
In[2]:=
Needs[ "DiscreteMath`Combinatorica`" ]
In[3]:=
?KSubsets
KSubsets[l,k] returns all subsets of set l containing exactly
k elements, ordered lexicographically.
In[4]:=
KSubsets[ nums, 2 ]
Out[4]=
{{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 3}, {2, 4},
{2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}, {4, 5}, {4, 6},
{5, 6}}
The Guide to Standrad Mathematica Packages provides brief
documentation of this package. It is documented in detail
in the book "Implementing Discrete Mathematics:
Combinatorics and Graph Theory with Mathematica" by Steven
Skiena (published by Addison Wesley).
I hope this helps.
--Ian
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Ian Collier
Wolfram Research, Inc.
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tel:(217) 398-0700 fax:(217) 398-0747 ianc at wolfram.com
Wolfram Research Home Page: http://www.wolfram.com/
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