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Unformatted text preview: P = x 1 1P + ( u1) P , for P P ( x, u ) , where x and u are indeterminates, by giving x n u k P ( x, u ) as an explicit expression in n and k. (b) (10 points) Construct a set P of combinatorial structures and a weight function for P such that [( P , )] o = P ( x, u ) . Note that the weight function must be of the form : P { , 1 , 2 , . . . } 2 : 7 ( 1 ( ) , 2 ( )) where 1 , 2 : P { , 1 , 2 , . . . } . and the form of the generating series P is P ( x, u ) = X P x 1 ( ) u 2 ( ) . ( Remark: You have been introduced to bivariate generating series (generating series in two indeterminates) in Math 239. ) 1...
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This note was uploaded on 11/18/2010 for the course CO 330 taught by Professor R.metzger during the Spring '05 term at Waterloo.
 Spring '05
 R.Metzger

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