Let S(n) = { a_1 + a_2 + ... + a_m |
m > 0,
a_1 + a_2 + ... + a_m = n, and
a_1 >= a_2 >= ... >= a_m >= 1 }
H(n,n) = |S(n)|
Search for "partition function" at
mathworld dot wolfram dot com
Example:
S(4) = { 4, 3+1, 2+2, 2+1+1, 1+1+1+1 }
H(4,4) = |S(4)| = 5
I remember deriving this recursive formula in the early seventies while taking a course in abstract algebra. I think it had to do with finding the number of groups of order k (up to an isomorphism). Anybody know if this is correct?
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