Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20120429 08:28:52
Generating FunctionsThis will be a thread for discussing GFs,their applications and uses,cool identities that can be proven using them and pretty much anything concerning them.Any questions about them are welcome and desirable. Last edited by anonimnystefy (20120429 09:26:59) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #2 20120429 12:05:38
Re: Generating Functions
The resulting nodes of the tree are compactly represented by the generating function. 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. #3 20120429 12:09:00
Re: Generating FunctionsI assume the T and H are tales and heads. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #4 20120429 12:12:32
Re: Generating FunctionsSometimes that is possible with a GF but only by a trick or two. It might be a little more like a Markov chain but that can be tricky too. 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. #5 20120429 12:15:35
Re: Generating FunctionsIt rhymes. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #6 20120429 16:56:27
Re: Generating FunctionsHi; 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. #7 20120429 20:52:57
Re: Generating FunctionsI think this is the one: The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #8 20120429 20:55:12
Re: Generating FunctionsWhen you square that you get the same matrix. 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. #9 20120429 21:08:54
Re: Generating FunctionsThen it is correct. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #10 20120429 21:12:33
Re: Generating FunctionsApparently, I was trying to get it to do the calculation on the right. 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. #11 20120429 21:20:45
Re: Generating FunctionsNo,squaring the matrix gives the probability of getting from the given state to another in two steps. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #12 20120429 21:27:18
Re: Generating FunctionsThat is what I am saying. The answer on the right needs something more than a matrix multiplication. But it is the tree answer. So my original statement that the tree can be represented entirely by a markov chain and matrix operations is not accurate. 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. #13 20120429 21:32:26
Re: Generating FunctionsYes,I agree. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #14 20120429 21:37:38
Re: Generating FunctionsSometimes there is an initial state vector. What vector do you want to use? 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. #15 20120429 21:38:58
Re: Generating FunctionsYes,I know. But it doesn't help. What matrix would you like as your output? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #16 20120429 21:41:06
Re: Generating FunctionsYou could do a scalar multiplication by A^(1) x A^(2) 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. #17 20120429 21:42:11
Re: Generating FunctionsWhat is A? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #18 20120429 21:44:25
Re: Generating FunctionsA is your matrix. A^(1) being the first level of the tree, A^(2) being the second level. 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. #19 20120429 21:46:17
Re: Generating FunctionsI don't understand what you want to do with that. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #20 20120429 21:49:22
Re: Generating FunctionsTrees are computed by mutiplying nodes down the branches. 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. #21 20120429 21:51:24
Re: Generating FunctionsOk,but what does that have to do with matrices? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #22 20120429 21:52:58
Re: Generating FunctionsInstead of the usual multiplication of 2 matrices, we could use an element by element multiplication of 2 matrices. 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. #23 20120429 21:57:22
Re: Generating FunctionsI don't think it would work for three steps. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #24 20120429 22:00:46
Re: Generating FunctionsSure it would. Element by element would give 1 / 8 for each branch. 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. #25 20120429 22:04:03
Re: Generating FunctionsBut there would be 8 branches! We only have a 2x2 matrix! The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment 