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MathGroup Archive 2005

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Re: Set construction with condition

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61722] Re: Set construction with condition
  • From: "Ray Koopman" <koopman at sfu.ca>
  • Date: Thu, 27 Oct 2005 05:01:53 -0400 (EDT)
  • References: <dj71qk$cmn$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In[1]:= <<DiscreteMath`Combinatorica`

In[2]:= StringJoin /@ Flatten[ Permutations /@ (
        Flatten@MapThread[Table[#1,{#2}]&,{{"1","X","2"},#}]& /@
        Select[Compositions[4,3],First@#<=2&] ), 1]

Out[2]= {2222,X222,2X22,22X2,222X,XX22,X2X2,X22X,2XX2,2X2X,22XX,XXX2,
         XX2X,X2XX,2XXX,XXXX,1222,2122,2212,2221,1X22,12X2,122X,X122,
         X212,X221,21X2,212X,2X12,2X21,221X,22X1,1XX2,1X2X,12XX,X1X2,
         X12X,XX12,XX21,X21X,X2X1,21XX,2X1X,2XX1,1XXX,X1XX,XX1X,XXX1,
         1122,1212,1221,2112,2121,2211,11X2,112X,1X12,1X21,121X,12X1,
         X112,X121,X211,211X,21X1,2X11,11XX,1X1X,1XX1,X11X,X1X1,XX11}

In[3]:= Sort@% == Sort@Select[StringJoin/@Tuples[{"1","X","2"},4],
                              StringCount[#,"1"]<=2&]
Out[3]= True

Edson Ferreira wrote:
> Dear Mathematica experts,
>
> I have this definition of L which generates a list of 81 elements:
>
> L=Flatten[Outer[StringJoin,{"1","X","2"},{"1","X","2"},{"1","X","2"},{"1","X","2"}]]
>
> How can I modify this definition in order to generate only elements in which there are a maximum of 2 characters "1"?
>
> Thanks!!!!!!!!!!!!!!
>
> PS.: I don't want to filter the entire 81 elements set AFTER the generation. I want to generate it with the desired elements.


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