Websercher GA this is actually for you.  I need the code(Maple) that
was used to generate the answers of 4 integers when summed give you
20,when order matters and when it does not.

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Clarification of Question by brkyrhrt99_00-ga on 21 Sep 2002 12:54 PDT

When order matters 1+2+3+14 and 1+3+2+14 are different.  When order
does not matter 1+2+3+14 and 1+3+2+14 are same.  Anyone can help me
out with this maple porgram help is appreciated.



Thanks

Hi brkyrhrt99_00:

I cleaned the file up a bit and added some comments for you. The Maple
input and comments are as follows. (Input lines have a > in front of
them, comments do not.)

> with(combinat);
Find all the compositions of 20 of 4 or less non-negative integers.
> allcomps := [op(composition(20,1)), op(composition(20,2)),
op(composition(20,3)), op(composition(20,4))];
Convert all the compositions to lists of 4 integers by padding with
zeroes.
> allcomps2 := [];
> for i from 1 to nops(allcomps) do
>    if nops(allcomps[i]) < 4 then
>       allcomps2 :=
[op(allcomps2),[0$(4-nops(allcomps[i])),op(allcomps[i])]]:
>    else
>       allcomps2 := [op(allcomps2),allcomps[i]]:
>    fi;
> od:
> allcomps2;
Sort inside the individual compositions.
> allcomps3 := map(sort, allcomps2):
> allcomps3;
Remove duplicate entries.
> alluncomps := [];
> for i from 1 to nops(allcomps3) do
>    if member(allcomps3[i], alluncomps) then
>       next;
>    else
>       alluncomps := [op(alluncomps), allcomps3[i]]:
>    fi:
> od:
> alluncomps;
How many are there?
> nops(alluncomps);
Find the number of possible permutations for each composition.
> map(numbperm, alluncomps, 4);
Sum the values up.
> convert(%, `+`);

I removed the output because it was really long. 

Hope this helps!

websearcher-ga

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Clarification of Answer by websearcher-ga on 21 Sep 2002 16:16 PDT

Because of the line breaking, some of the input lines start on lines
without the > character. However, it should still be clear which lines
are comments.

websearcher-ga

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Request for Answer Clarification by brkyrhrt99_00-ga on 22 Sep 2002 09:09 PDT

is this for when order matters or when it does not.? and what would be
the code for the other case.  THANK YOU>

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Clarification of Answer by websearcher-ga on 22 Sep 2002 10:09 PDT

Actually, it is for computing *both* when ordering does and when it
doesn't count. In my method, you must compute without ordering first
in order to then compute with ordering. One follows from the other.

I've added a few additional comments to help you understand better. 

> with(combinat);
Find all the compositions of 20 of 4 or less non-negative integers.
> allcomps := [op(composition(20,1)), op(composition(20,2)), 
> op(composition(20,3)), op(composition(20,4))];
Convert all the compositions to lists of 4 integers by padding with
zeroes.
> allcomps2 := [];
> for i from 1 to nops(allcomps) do
>    if nops(allcomps[i]) < 4 then
>       allcomps2 := [op(allcomps2),
>                    [0$(4-nops(allcomps[i])),
>                    op(allcomps[i])]]:
>    else
>       allcomps2 := [op(allcomps2),allcomps[i]]:
>    fi;
> od:
> allcomps2;

Sort inside the individual compositions so that we can later eliminate
duplicate entries.
> allcomps3 := map(sort, allcomps2):
> allcomps3;
Remove duplicate entries to find the number of compositions when
ordering does not count.
> alluncomps := [];
> for i from 1 to nops(allcomps3) do
>    if member(allcomps3[i], alluncomps) then
>       next;
>    else
>       alluncomps := [op(alluncomps), allcomps3[i]]:
>    fi:
> od:
> alluncomps;
How many are there?
> nops(alluncomps);

Find the number of possible permutations for each individual
composition in order to compute how many compositions there are when
ordering does count.
> map(numbperm, alluncomps, 4);
Sum the values up.
> convert(%, `+`);

I have also put a copy of the complete document (output included)
online if you want to view it.

http://www.lucidmatrix.com/uploads/20output.txt 

websearcher-ga

Excellent.  Thank you very much