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**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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.**

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**zetafunc.****Guest**

No news, this has been a pretty dry day.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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.**

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**zetafunc.****Guest**

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.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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.**

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**zetafunc.****Guest**

The Higgs boson, I think.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

I am getting 1216 for the answer.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Okay, thank you.

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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)*

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

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