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Unformatted text preview: A (where the weight of the empty set is dened to be zero). (c) Write down the generating function for S where the weight of a subset A is dened to be the sum of the elements in A . 4. Let N = { , 1 , 2 , 3 , . . . } , and let the weight of n N be w ( n ) = n/ 4 if 4  n, n/ 2 if n 2(mod 4) , n otherwise. Find the generating function N ( x ) in the form p ( x ) q ( x ) where p ( x ) and q ( x ) are polynomials. 5. Find the inverse of the formal power series A ( x ) = X n n X k =0 20 k (2) nk x n . Write the inverse in the form p ( x ) q ( x ) where p ( x ) and q ( x ) are polynomials. (Hint: rst try to write A ( x ) as a product of two other formal power series.) 1...
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This note was uploaded on 10/23/2009 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.
 Spring '09
 M.PEI
 Algebra, Combinatorics, Integers, Binomial

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