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## #9051 2013-03-12 08:15:36

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

That is okay, we are all busy at some point.

## #9052 2013-03-12 08:29:46

bobbym

Online

### Re: Linear Interpolation FP1 Formula

I still did not get the can opener though.

Any news?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9053 2013-03-12 08:31:17

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

No news, this has been a pretty dry day.

## #9054 2013-03-12 08:32:56

bobbym

Online

### Re: Linear Interpolation FP1 Formula

Sometimes that is good. No news is much better than bad news.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9055 2013-03-12 08:52:38

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Been talking to my male friends though, I am going to a Steven Weinberg lecture in two days' time. Hopefully there is not a mile-long queue like last time.

## #9056 2013-03-12 08:54:13

bobbym

Online

### Re: Linear Interpolation FP1 Formula

That is very good. What is he speaking about?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9057 2013-03-12 09:16:59

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

The Higgs boson, I think.

## #9058 2013-03-12 09:22:45

bobbym

Online

### Re: Linear Interpolation FP1 Formula

He is a good lecturer, an interesting guy. Especially when he is talking about philosophy.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9059 2013-03-12 10:24:27

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

I have never heard him speak in person, I have only watched him on YouTube. You have seen him live?

## #9060 2013-03-12 10:38:12

bobbym

Online

### Re: Linear Interpolation FP1 Formula

No, I have never seen him in person either. I have seen him in documentaries.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9061 2013-03-12 11:00:28

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Me too. I have heard him talk about the laws of nature most of the time though.

Having another hard time with a combinatorics problem, that I do not know how to set up the GF of... or even if there exists a GF.

## #9062 2013-03-12 11:33:08

bobbym

Online

### Re: Linear Interpolation FP1 Formula

Post the problem and who knows what will happen. Could be the end of the world or maybe just a solution of sorts.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9063 2013-03-12 17:58:43

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

How many numbers from 10,000 to 100,000 (inclusive) contain only two different digits? (e.g. 32332, 11114, but not 10002)

I don't understand how to set up the GF for this problem...

## #9064 2013-03-12 18:20:42

bobbym

Online

### Re: Linear Interpolation FP1 Formula

Hi;

I am getting 1216 for the answer.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9065 2013-03-12 18:23:29

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

That is correct... how did you get the GF for this? The thing I'm having trouble representing is the constraint that only 2 different numbers are allowed. I tried representing each possible digit of a 5-digit number with polynomials of degree x^9, but I didn't know what to do with it...

## #9066 2013-03-12 18:26:03

bobbym

Online

### Re: Linear Interpolation FP1 Formula

These type are always a little bit tricky. I will start to work on it as soon as I handle this spammer.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9067 2013-03-12 18:32:54

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Okay, thank you.

So, you did this one by hand/with a more systematic approach?

## #9068 2013-03-12 18:47:19

bobbym

Online

### Re: Linear Interpolation FP1 Formula

There are other ways to get at it by standard combinatorics and experimental methods.

No luck with the gf though. with hand methods.

Quite easy using a CAS:

With n being the number of digits in the number.

Closed form:

Linear recurrence:

with

GF:

I am going to take a little break.

Last edited by bobbym (2013-03-12 20:50:46)

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9069 2013-03-13 05:17:36

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

I keep staring at that and I haven't got a clue how you got that...

## #9070 2013-03-13 09:12:56

bobbym

Online

### Re: Linear Interpolation FP1 Formula

Hi;

Computational mathematics has solved the problem of getting those to a very high degree.

There does not appear to be any way by hand methods that I can discover.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9071 2013-03-13 09:30:57

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Oh, okay... thank you, though. I guess the other problem is deciding when to use a GF and when not to... I downloaded a book called 'Generatingfunctionology', I will read it and see if I can understand how these things work a bit more. I've heard it is good.

Nothing from adriana, hmm. It has been 3 days. I did not expect such a sharp decline.

## #9072 2013-03-13 09:43:47

bobbym

Online

### Re: Linear Interpolation FP1 Formula

That is a good book. Herbert passed away a little while back, he was the best all around mathematician of today.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9073 2013-03-13 09:46:20

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

I had never heard of him previously, unfortunately... but it does look like a great read. It seems to cover everything I would need to know -- one thing I was curious about is why exponential generating functions are used for permutations, and ordinary generating functions are used for combinations. I just learned it without understanding how someone found out that we could use them.

## #9074 2013-03-13 09:53:23

bobbym

Online

### Re: Linear Interpolation FP1 Formula

Exponential gf's are made from the e^x series. Each term has a factorial. By themselves they do not count permutations. You need to multiply the correct power of x by the factorial of the power.

The first couple of chapters are a very good introduction after that it does stiffen up.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9075 2013-03-13 10:02:00

zetafunc.
Guest

### Re: Linear Interpolation FP1 Formula

Oh, of course... that makes so much sense, so they just needed to find a series that combined an OGF with factorials in it.