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You are not logged in. #1 20110112 22:38:19
Race with possibility of ties (permutations!)How many ways are there for a horse race with 6 horses to finish if ties are possible? "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #2 20110113 00:21:24
Re: Race with possibility of ties (permutations!)I think the best way to do this is to build up from one horse. Why did the vector cross the road? It wanted to be normal. #3 20110113 00:48:19
Re: Race with possibility of ties (permutations!)Mathsy, we must treat horses to be distinct... E.g. there are 13 ways for 3 horses to finish the race. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #4 20110113 03:46:59
Re: Race with possibility of ties (permutations!)Hi gAr; 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 20110113 03:58:27
Re: Race with possibility of ties (permutations!)Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #6 20110113 04:27:39
Re: Race with possibility of ties (permutations!)Hi gAr; Where that big S are stirling numbers of the second kind. There is no known closed form for this problem. 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 20110113 05:01:29
Re: Race with possibility of ties (permutations!)Wow! I see, Stirling's number of second kind. Last edited by gAr (20110113 05:05:17) "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #8 20110113 05:04:21
Re: Race with possibility of ties (permutations!)Hi; 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 20110113 05:08:11
Re: Race with possibility of ties (permutations!)Yes, I went exactly to those two pages before replying "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #10 20110113 05:10:56
Re: Race with possibility of ties (permutations!)Then you saw this cute one: 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 20110113 13:50:37
Re: Race with possibility of ties (permutations!)Yes, that's cute indeed! Amazing... "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #12 20110113 14:22:45
Re: Race with possibility of ties (permutations!)Hi gAr and bobbym; Last edited by 4DLiVing (20110114 12:38:14) #13 20110113 15:07:38
Re: Race with possibility of ties (permutations!)
Hi 4DLiVing; These are the stirling numbers of the second kind. Now for an 8 horse trace. That is the formula I posted already. When we expand it out we get. Hi 4DLiVing; As a partial answer to your question although there is a pattern in the above table there is no closed form known for it. 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. #14 20110113 16:37:37
Re: Race with possibility of ties (permutations!)Hi 4DLiVing, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #15 20110113 17:14:17
Re: Race with possibility of ties (permutations!)Hi;
I do not think it has been proven but no closed form has been found for that recursion.
Yes, there are approximations for large n 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. #16 20110113 18:22:14
Re: Race with possibility of ties (permutations!)Thanks bobbym, that's nice. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #17 20110113 18:35:26
Re: Race with possibility of ties (permutations!)What are you using to do the calculations I am getting good results for even small numbers for instance: 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. #18 20110113 18:53:10
Re: Race with possibility of ties (permutations!)I was checking the difference. On seeing its order of magnitude, I felt like that... Last edited by gAr (20110113 18:55:42) "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #19 20110113 19:01:23
Re: Race with possibility of ties (permutations!)Hi gAr; 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. #20 20110113 19:36:05
Re: Race with possibility of ties (permutations!)Thank you bobbym. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #21 20110113 22:09:14
Re: Race with possibility of ties (permutations!)Thanks bobbym and gAr for looking into the triangle for me. #22 20110113 22:26:09
Re: Race with possibility of ties (permutations!)Yes, we are all here to enjoy the math! "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #23 20110114 07:45:28
Re: Race with possibility of ties (permutations!)Hi gAr; It was not as bad as we thought because we are using it wrong. There are improvements to it but the amount calculation grows with each one. 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. #24 20110114 14:02:10
Re: Race with possibility of ties (permutations!)Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #25 20110114 20:04:07
Re: Race with possibility of ties (permutations!)Hi; It also might blow up for some particular values. It was done using the Riemann Rearrangement Algorithm. 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. 