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#9051 2013-03-11 09:15:36

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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

#9052 2013-03-11 09:29:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9053 2013-03-11 09:31:17

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

No news, this has been a pretty dry day.

#9054 2013-03-11 09:32:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9055 2013-03-11 09:52:38

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 2013-03-11 09:54:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9057 2013-03-11 10:16:59

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

The Higgs boson, I think.

#9058 2013-03-11 10:22:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9059 2013-03-11 11:24:27

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 2013-03-11 11:38:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9061 2013-03-11 12:00:28

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 2013-03-11 12:33:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9063 2013-03-11 18:58:43

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 2013-03-11 19:20:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9065 2013-03-11 19:23:29

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 2013-03-11 19:26:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9067 2013-03-11 19:32:54

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Okay, thank you.

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

#9068 2013-03-11 19:47:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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 (2013-03-11 21:50:46)


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9069 2013-03-12 06:17:36

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

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

#9070 2013-03-12 10:12:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9071 2013-03-12 10:30:57

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 2013-03-12 10:43:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9073 2013-03-12 10:46:20

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 2013-03-12 10:53:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,466

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9075 2013-03-12 11:02:00

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.

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