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MathGroup Archive 1996

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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

-----------------------------------------------------------
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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