
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 10th, 2010, 09:30 PM  #1 
Newbie Joined: Oct 2009 Posts: 26 Thanks: 0  Number of Necklace/Bracelets With Fixed Number of Beads
We can compute the total number of kary necklaces/bracelets of length n using the Euler totient function: http://en.wikipedia.org/wiki/Necklace_% ... atorics%29 Are there formulas for the number of kary necklaces/bracelets when the number of beads for each color is fixed? For example, the number of necklaces of length 5, made up of three colors (red, green, blue), with 2 red beads, 2 green beads, and 1 blue bead. etc. 
June 12th, 2010, 06:57 PM  #2 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: Number of Necklace/Bracelets With Fixed Number of Beads
Yes, we can. But I don't completely remember how (it's been 2 years since I last saw it!) I believe there is some information on approaches to this sort of problem in Wilf's Generatingfunctionology. 
June 13th, 2010, 01:03 AM  #3 
Newbie Joined: Jul 2009 From: England Posts: 25 Thanks: 0  Re: Number of Necklace/Bracelets With Fixed Number of Beads
This problem seems similar to 'How many ways can you colour the sides of a cube using 3 colours' and we used group theory, orbits and stabilizers.


Tags 
beads, fixed, necklace or bracelets, number 
Search tags for this page 
in how many ways can a bracelet of 10 different beads be made?,the number of distinct bracelet of five beads made up of red,green blue beads,bracelets number theory,the number of distinct bracelets of five beads
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Number system  proving 9 digit number not divisible by 5  sachinrajsharma  Number Theory  7  April 29th, 2013 06:49 AM 
Probability Beads and bracelets.  azizlwl  Advanced Statistics  3  March 10th, 2012 12:17 AM 
Number of circular bracelets  rudrax  Algebra  3  June 8th, 2011 10:25 PM 
find unique n number combination in total n number  jsonliu  Algebra  3  May 18th, 2010 06:01 PM 
Convert binary range with fixed number of zeros/ones  hansdejong  Number Theory  2  June 30th, 2009 05:15 PM 