Combination/Permutation questions

*To*: mathgroup at smc.vnet.net*Subject*: [mg37436] Combination/Permutation questions*From*: michael_chang86 at hotmail.com (Michael Chang)*Date*: Tue, 29 Oct 2002 00:09:38 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi everyone, I'm running Mathematica 4.1 on Windoze XP, and have some newbie combination/permutation questions, and am hoping that the collective wisdom of this newsgroup can help/guide me out! ;) First, suppose that I have 4 objects, a, b, c, and d, respectively. How can I generate the permutation set when chosing, say, only *2* elements. In[1]:= Permutations[{a,b,c,d}] gives me the permutation set when choosing *all* 4 objects ... :( Second, for the same four objects (a,b,c,d), to generate the *combination* set (with 2 elements), I use: In[2]:= Needs["DiscreteMath`Combinatorica`"]; In[3]:= cset=KSubsets[{a,b,c,d},2] and this generates the expected 6 combinatorial pairs ({{a,b},{a,c},{a,d},{b,c},{b,d},{c,d}}). What I'd like to do next is add each combinatorial set, and I am able to do this correctly via: In[4]:= Plus@@Transpose[cset] to obtain {a+b,a+c,a+d,b+c,b+d,c+d}. My problem lies in the fact that now, I'd like to be able to allow *each* (a,b,c,d) element to be either plus, or minus (in reality, I'm trying to generate combinatorial adds/minuses for *functions* (a,b,c,d)), and to still generate the 'sum' of the cominatorial set. So for instance, in my current example, for the *first* {a,b} combinatorial pair, I'd like to be able to generate In[5]:= Plus@@Transpose[Partition[Flatten[Outer[List,{a,-a},{b,-b}]],2]] (which generates {a+b,a-b,-a+b,-a-b}) ... only I'd like this to be somehow done automatically for *each* combinatorial pair (and, for the more general case when I generate combinatorial sets involving only 'k' elements). I've struggled with this for a while, and am only able to generate such a list *manually* for each of my six original combinatorial pairs ... a tedious, and somewhat tiresome procedure! :( Is there a way of 'easily' doing this?!? With my newly generated list (having 4*6 'elements'), how can I also go about finding which expressions involve/use only, say, 1 Minus? Is there an 'easy' way of doing this too? (For instance, I'd like to then 'filter' for (a-b) and (b-a) ...) (Perhaps the count of 1 Minus is a little contrived for this example here, but for the more general case I'll probably be considering, I might need to filter for, say, (longer) expressions involving 2 Minuses (say).) My apologies in advance for my rather long email, but as always, any feedback and help would be most welcome and appreciated! Thanks, Michael

**Follow-Ups**:**Re: Combination/Permutation questions***From:*Tomas Garza <tgarza01@prodigy.net.mx>