Re: Combination/Permutation questions
- To: mathgroup at smc.vnet.net
- Subject: [mg37545] Re: Combination/Permutation questions
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Mon, 4 Nov 2002 02:44:27 -0500 (EST)
- References: <apvbvk$rni$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Michael,
For the latter part of your question:
Needs["DiscreteMath`Combinatorica`"];
data={a,b,c,d};
Flatten[{#+#2,#1-#2,-#1+#2,-#1-#2}&@@
Transpose[KSubsets[data,2]]]
{a+b,a+c,a+d,b+c,b+d,c+d,a-b,a-c,a-d,b-c,b-d,
c-d,-a+b,-a+c,-a+d,-b+c,-b+d,-c+d,-a-b,-a-c,-a-d,-b-c,-b-d,-c-d}
Flatten[{#1-#2,-#1+#2}&@@
Transpose[KSubsets[data,2]]]
{a-b,a-c,a-d,b-c,b-d,c-d,-a+b,-a+c,-a+d,-b+c,-b+d,-c+d}
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"Michael Chang" <michael_chang86 at hotmail.com> wrote in message
news:apvbvk$rni$1 at smc.vnet.net...
> 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
>