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 ( nk + 3)2 nk2 times among all the 2 n1 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 = (42 + 3)2 422 times. 1 Rooks can attack pieces in their same row or column only....
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 Fall '10
 Vetter
 Rooks, diﬀerent colored rooks

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