February 11th, 2012, 08:21 AM  #1 
Newbie Joined: Feb 2012 Posts: 12 Thanks: 0  PERMUTATION
Hi to everyone.... I would like to know which is the permutation 4661 of the elements G = {1,2,3,4,5,6,7} I have search for the formula around the internet but I could not find it... So I hope any one can help about this solution. Thank you, and I hope I will get any answer ASAP 
February 11th, 2012, 01:25 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: PERMUTATION Hello, toli! Quote:
Your question is not clear, but I suspect I know what you mean. Suppose we write all 5,040 permutations of {1,2,3,4,5,6,7} in increasing order. What is the 4661st number of the list? Is that it?  
February 11th, 2012, 03:01 PM  #3 
Newbie Joined: Feb 2012 Posts: 12 Thanks: 0  Re: PERMUTATION
when we calculate the 7! "FACTORIAL" it is true that we have 5040 permutations and that permutation number is 7654321... so I need to find the permutation 4661 " LET'S SUPPOSE IT IS 6453217 " i guess it is a little bit better written. I have tried to find the way out of the solution but I couldn't find any Formula on my book or in the internet... so I hope you can help me with this exam... thank you once again soroban 
February 11th, 2012, 04:56 PM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: PERMUTATION Hello, toli! You're still not very clear. Can you tell me whether my interpretation is correct? Quote:
IF my interpretation is correct, and we are looking for the 4661th number on the list of permutations, [color=beige]. . [/color]there is a procedure for determining this number. It was discovered by a high school student in the 1960's and is very complicated. But I won't explain it if I'm misreading the problem.  
February 11th, 2012, 05:03 PM  #5 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: PERMUTATION
You can solve it very easily with PARI/GP if soroban's interpretation is right. Look at numtoperm.

February 12th, 2012, 04:22 AM  #6 
Newbie Joined: Feb 2012 Posts: 12 Thanks: 0  Re: PERMUTATION
CRGreathouse: thank you for giving me your program, I am downloading it now and I will let you know if it works or no... which I think it will... 
February 12th, 2012, 04:38 AM  #7 
Newbie Joined: Feb 2012 Posts: 12 Thanks: 0  Re: PERMUTATION
Soroban I will give you one of the exam that's on my book I hope I will explain it as best as I can so maybe you do have any solution because I really have no Idea about this one... Determine permutation 604 of the elements 1,2,3,4,5,6. It is known that form 6 element's we have 6! = 720 Permutation's Permutation from 1 to 120 number 1 is the first digit, similar act is with the other permutation; With other words, Permutation 601 is: 612345 >>>>>>> permutation 601 then we have 612354 >>>>>>> permutation 602 612435 >>>>>>> permutation 603 612453 >>>>>>> this is the permutation that we need for these exam... BUT WHEN IT COMES TO THE QUESTION FOR PERMUTATIONS 4661 FOR THE ELEMENTS G = {1,2,3,4,5,6,7} I AM STUCK AND I DON'T KNOW HOW TO FIGURE IT OUT... I HOPE THIS IS HELPFULLY FOR YOU Soroban. 
February 12th, 2012, 05:05 AM  #8 
Newbie Joined: Feb 2012 Posts: 12 Thanks: 0  Re: PERMUTATION
Soroban I have found the Permutation of 4661 that corresponds to the elements of 1,2,3,4,5,6,7 and that permutation is 7,3,6,1,5,2,4 but what I need is the steps on how to find the solution of these given question... I hope you know what to do... thank you. 
February 12th, 2012, 05:10 AM  #9 
Newbie Joined: Feb 2012 Posts: 12 Thanks: 0  Re: PERMUTATION
CRGreathouse: I have tried to find the short digits for the program you advice me to use it but I really could not find any solution maybe just because I didn't know how to use otherwise thank you a lot for help I appreciate what you have done for me. Thank you again. 
February 12th, 2012, 01:13 PM  #10 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: PERMUTATION Code: > ?numtoperm numtoperm(n,k): permutation number k (mod n!) of n letters (n Cinteger). > numtoperm(7, 4661) %1 = [4, 1, 6, 2, 3, 5, 7] 

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