Generating Functions

bobbym · 2012-04-29 16:55:33

Yes, that is all there is to solving those types of permutation problems. Easy with generating functions hard with the school method.

anonimnystefy · 2012-04-29 16:58:00

Seems so. Sorry for asking this,but,how do we prove that the answer we get is what we wanted?

bobbym · 2012-04-29 17:03:34

Remember the guy who did not want to do anymore math so he learned computers. That is how.

anonimnystefy · 2012-04-30 00:36:56

You mean you?

Computers again? I don't think that using this in class will be any good if I can prove it gets the right answers without a hand method.Ironic,huh?

bobbym · 2012-04-30 00:38:30

That does not make sense.

anonimnystefy · 2012-04-30 00:39:47

If I am going to use this method in class,I need to be able to show it works by hand methods.It really doesn't make sense,but it s how it is.

bobbym · 2012-04-30 00:40:52

Nope, the computer backs up the hand method.

People who only use hand methods rarely get a combinatorics problem correct.

anonimnystefy · 2012-04-30 00:41:48

Either way-Is there a hand proof that using GFs like that does the job right?

bobbym · 2012-04-30 00:44:27

Different question, they are both hand methods. That is why I do not remember them.

anonimnystefy · 2012-04-30 00:45:34

I don't understand you.

bobbym · 2012-04-30 00:55:00

Talking about gfs is different then post #77

anonimnystefy · 2012-04-30 00:57:11

No,I meant-How do I prove that the answer we got with GFs is the the correct one by hand methods?

bobbym · 2012-04-30 00:58:48

Prove? That is a funny word. Generally when you do a piece of algebra you do not have to prove it. The work is the proof.

anonimnystefy · 2012-04-30 01:07:55

Well,I am not sure if my prof is gonna be happy if I don't show somehow that the number that I got using GFs is correct.

Can you look something up to tell me what is wrong with this Maxima code:

CombGF(list):=block([i,j,a,m,s],
i=1,
m=1,
while i<=length(list) do
[
a=get(list,i),
j=1,
s=0,
while j<=a do
  s=s+x^j,
m=m*s,
i=i+1
],
return(m)
);

It compiles,but doesn't run properly.

bobbym · 2012-04-30 01:13:02

You wrote it? What is the output supposed to look like?

anonimnystefy · 2012-04-30 01:17:11

Yes,I wrote it.

It should give me a generating function in x.E.g.:

CombiGF([1,1,1,2]);

should give:

PS I changed the code line:

s=s+x^j,

to

s=s+x^j/j!,

Last edited by anonimnystefy (2012-04-30 01:17:39)

bobbym · 2012-04-30 01:26:36

Expanded out?

anonimnystefy · 2012-04-30 01:27:41

Doesn't matter.I can expand it later if I it doesn't expand itself on output.

bobbym · 2012-04-30 01:29:33

Question first:

How would you display this:

anonimnystefy · 2012-04-30 01:31:27

I don't know what you mean.

bobbym · 2012-04-30 01:34:43

Same thing. I wish to have the gf of a single dice. How do you do it?

anonimnystefy · 2012-04-30 01:37:58

It doesn't do the ordinary GF.It does the exp GF for the type of problem you've given me before.

bobbym · 2012-04-30 01:39:10

What I am saying is would you write a loop like you have done to do that?

anonimnystefy · 2012-04-30 01:42:19

The code in #89 would be for that.

And my input would be:

CombiGF([6])

bobbym · 2012-04-30 01:44:18

Why are you using a procedural form in a CAS?

Math Is Fun Forum

#76 2012-04-29 16:55:33

Re: Generating Functions

#77 2012-04-29 16:58:00

Re: Generating Functions

#78 2012-04-29 17:03:34

Re: Generating Functions

#79 2012-04-30 00:36:56

Re: Generating Functions

#80 2012-04-30 00:38:30

Re: Generating Functions

#81 2012-04-30 00:39:47

Re: Generating Functions

#82 2012-04-30 00:40:52

Re: Generating Functions

#83 2012-04-30 00:41:48

Re: Generating Functions

#84 2012-04-30 00:44:27

Re: Generating Functions

#85 2012-04-30 00:45:34

Re: Generating Functions

#86 2012-04-30 00:55:00

Re: Generating Functions

#87 2012-04-30 00:57:11

Re: Generating Functions

#88 2012-04-30 00:58:48

Re: Generating Functions

#89 2012-04-30 01:07:55

Re: Generating Functions

#90 2012-04-30 01:13:02

Re: Generating Functions

#91 2012-04-30 01:17:11

Re: Generating Functions

#92 2012-04-30 01:26:36

Re: Generating Functions

#93 2012-04-30 01:27:41

Re: Generating Functions

#94 2012-04-30 01:29:33

Re: Generating Functions

#95 2012-04-30 01:31:27

Re: Generating Functions

#96 2012-04-30 01:34:43

Re: Generating Functions

#97 2012-04-30 01:37:58

Re: Generating Functions

#98 2012-04-30 01:39:10

Re: Generating Functions

#99 2012-04-30 01:42:19

Re: Generating Functions

#100 2012-04-30 01:44:18

Re: Generating Functions

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