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The Sieve Formula
Posted:
Dec 2, 2008 1:24 AM


I have a problem that I am working on that I am having a lot of trouble with, perhaps you guys can help me out.
In how many ways can we list the digits {1,1,1,2,2,3,4,5} so that two identical digits are not in consecutive positions?
Also, one other problem dealing with the same topic:
How many partitions of [8] satisfy the three following properties. 1.) 1 and 2 are in different parts, 2.) 2 and 3 are in different parts, and 3.) 7 and 8 are in different parts. Recall that the nth Bell number counts the number of set partitions of [n]. The first few terms of B(n) are listed below:
{B(n)}n>=1 = {1,2,5,15,52,203,877,4140,...}
Thanks a lot for the help guys, I really appreciate it.



