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#26 2012-04-29 00:10:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Yes, that is going to be a problem.


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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#27 2012-04-29 00:15:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Maybe we can use something like adjoint?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#28 2012-04-29 00:20:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

I forget that one every once in a while. Like a permanent but aren't they hard to compute?


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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#29 2012-04-29 00:25:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Whoops that is not what I meant. I have a little problem with tachnical matrix terms.

Couldn't we just add another column at each iteration?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#30 2012-04-29 00:30:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

It is getting too unwieldy. If we needed the 1000th level that matrix would be huge.


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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#31 2012-04-29 00:32:25

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Well there is no other way to represent it all.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#32 2012-04-29 07:27:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Not that I know of right now.


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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#33 2012-04-29 07:30:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

I meant with a matrix.

Here's another topic:"Do you know any uses of exponental GFs in math problems? Show  example."


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#34 2012-04-29 07:32:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Have you seen the problems gAr and I first worked on?


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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#35 2012-04-29 07:34:25

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

No. I wasn't around at the time. Can you send me a link of one of those problems?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#36 2012-04-29 07:36:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

How about you work on one I give you and see if you can solve it?


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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#37 2012-04-29 07:40:36

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Sure! I love new problems!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#38 2012-04-29 07:53:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

How many arrangements of 6 letters can be made from numismatics?


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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#39 2012-04-29 07:55:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

I presume you mean the word.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#40 2012-04-29 08:04:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Yes, they are always structured liked that. Numismatics how many arrangements of 6 letters?


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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#41 2012-04-29 08:05:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

What do you mean by arrangement? Can I use double letters twice?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#42 2012-04-29 08:10:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Yes, only the amounts you have there. Here is a 6 letter word MMIISS


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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#43 2012-04-29 08:11:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

Is it 11!/8 ?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#44 2012-04-29 08:16:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

No, that number is too big.


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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#45 2012-04-29 08:22:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

This problem is harder than I originally thought.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#46 2012-04-29 08:24:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

That is an easy one.


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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#47 2012-04-29 08:26:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

I don't know how to solve it.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#48 2012-04-29 08:33:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions


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.

Offline

#49 2012-04-29 08:40:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,536

Re: Generating Functions

So that's the GF! I couldn't think of a way to get that.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#50 2012-04-29 08:41:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,807

Re: Generating Functions

Then try another one! 8 letter words from Mississippi.


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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