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Re: Re: NthSubset function of Combinatorica package

• To: mathgroup at smc.vnet.net
• Subject: [mg88836] Re: [mg88835] Re: NthSubset function of Combinatorica package
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 19 May 2008 05:14:12 -0400 (EDT)
• References: <g0o7p3$ebb$1@smc.vnet.net> <200805181134.HAA23926@smc.vnet.net>

On 18 May 2008, at 20:34, Szabolcs Horv=E1t wrote:

> Roman wrote:
>> Hello all:
>>
>> Do you know how the function "NthSubset" of the Combinatorica package
>> works? If you can point me to a description of the algorithm, that
>> would be very helpful.
>>
>
> You can read the source code of all standard packages.  Go to
> $InstallationDirectory/AddOns/Packages/Combinatorica, and search for
> NthSubset in Combinatorica.m.  You will find that it just calls the
> built-in Subsets function.
>
> Subsets[] is built-in, so we cannot see its implementation.  But there
> are several subset-related functions in Combinatorica, such as 
> KSubsets,
> whose code is available.  You can check those.
>
> Or just search the web.  Here's the first hit I got for "generating
> subsets":
>
> http://compprog.wordpress.com/2007/10/10/generating-subsets/
>
> And a Mathematica implementation of this algorithm (for generating all
> subsets):
>
> subsets[l_List] :=
>  Table[Pick[l, IntegerDigits[k, 2, Length[l]], 1],
>    {k, 0, 2^Length[l] - 1}]
>


However, note that

Subsets[Range[1000], All, {1100}]

  ( {{1, 100}} )

returns the answer immediately while

Subsets[Range[1000], All]

gives a rather different answer ... so the former certianly does make 
use of the latter.

Andrzej Kozlowski

• References:
  • Re: NthSubset function of Combinatorica package
    • From: Szabolcs Horvát <szhorvat@gmail.com>