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MathGroup Archive 1999

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Re: Binary System Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18679] Re: [mg18621] Binary System Problem
  • From: Robert Pratt <rpratt at math.unc.edu>
  • Date: Thu, 15 Jul 1999 01:45:59 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Needs["DiscreteMath`Combinatorica`"]

toBinary[lis_List,n_]:=Table[If[MemberQ[lis,i],1,0],{i,1,n}]

frieder[n_,k_]:=Map[toBinary[#,n]&,KSubsets[Range[n],k]]

frieder[5,4]
{{1,1,1,1,0},{1,1,1,0,1},{1,1,0,1,1},{1,0,1,1,1},{0,1,1,1,1}}

You can go back and forth between the lists of binary digits and the
decimal numbers as follows.

Map[FromDigits[#,2]&,frieder[5,4]]
{30,29,27,23,15}

Map[IntegerDigits[#,2]&,%]
{{1,1,1,1,0},{1,1,1,0,1},{1,1,0,1,1},{1,0,1,1,1},{1,1,1,1}}

Rob Pratt
Department of Mathematics
The University of North Carolina at Chapel Hill
CB# 3250, 331 Phillips Hall
Chapel Hill, NC  27599-3250

rpratt at math.unc.edu

http://www.math.unc.edu/Grads/rpratt/

On Tue, 13 Jul 1999, Frieder Schweigert wrote:

> Hi,
> 
> does anybody know an algorithm or generating system for
> those binary numbers with a fix amount of '1's,
> for example (four times '1'):
> 
>  1111
> 10111
> 11011
> 11101
> 11110
> 



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