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Unformatted text preview: concerns Chapter 3. 5 Without using any asymptotic bounds for p ( n ), prove that p ( n ) grows faster than any polynomial. That is, if f ( n ) is any polynomial, prove that there is some integer N such that p ( n ) > f ( n ) for all n > N . 6 Suppose that 1 k < n . Prove that the part k occurs a total of ( n-k + 3)2 n-k-2 times among all the 2 n-1 compositions of n . For example, if n = 4 and k = 2, then the part 2 occurs once in 2 + 1 + 1, 1 + 2 + 1, and 1 + 1 + 2, and twice in 2 + 2, for a total of 5 = (4-2 + 3)2 4-2-2 times. 1 Rooks can attack pieces in their same row or column only....
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This note was uploaded on 12/10/2011 for the course MAD 4203 taught by Professor Vetter during the Fall '10 term at University of Florida.
- Fall '10