December 4, 2008 at 12:43 am
Given an integer n, it is possible to represent it as the sum of one or more positive integers.This representations called a partition if the order of the x; is of no consequence. Thus two partitions of an integer n are distinct if they differ with respect to the x; they contain.
For example, there are seven distinct partitions of the integer 5:
5=5
5=4+1
5=3+2
5=3+1+1
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1
The total is 7
December 5, 2008 at 9:24 am
And your objective is? Generating the list? Or just determining the number of partitions, given N ? Also, have you made any attempt at whatever it is you want to accomplish, and if so, what code or T-SQL did you write?
Steve
(aka smunson)
:):):)
Steve (aka sgmunson) 🙂 🙂 🙂
Rent Servers for Income (picks and shovels strategy)
December 5, 2008 at 9:52 am
This doesn't look particularly easy... Take a look at the following links:
http://en.wikipedia.org/wiki/Partition_of_an_integer#Partition_function
http://www.research.att.com/~njas/sequences/A000041
I'm pretty good with numbers, but the math in Rademacher's series is more than a bit too complex for me. I was hoping for a scalar solution, at least for the number of partitions, but that appears impractical. However, generating the partitions themselves might be approachable using a recursive CTE, but it won't be easy. You are likely going to want to have a "Tally table" of numbers. Look that up on this forum. Somehow, this looks like one of those cases where a WHILE loop is going to be essential. Anyone feel like proving me wrong? I'd love to see the result...
Steve
(aka smunson)
:):):)
Steve (aka sgmunson) 🙂 🙂 🙂
Rent Servers for Income (picks and shovels strategy)
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