Unformatted text preview: P = x Â± 1 1P + ( u1) P Â² , for P â‰¡ P ( x, u ) , where x and u are indeterminates, by giving Â³ x n u k Â´ 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 Ï‰ for P such that [( P , Ï‰ )] o = P ( x, u ) . Note that the weight function Ï‰ must be of the form Ï‰ : P â†’ { , 1 , 2 , . . . } 2 : Ïƒ 7â†’ ( Ï‰ 1 ( Ïƒ ) , Ï‰ 2 ( Ïƒ )) where Ï‰ 1 , Ï‰ 2 : P â†’ { , 1 , 2 , . . . } . and the form of the generating series P is P ( x, u ) = X Ïƒ âˆˆP x Ï‰ 1 ( Ïƒ ) u Ï‰ 2 ( Ïƒ ) . ( Remark: You have been introduced to bivariate generating series (generating series in two indeterminates) in Math 239. ) 1...
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 Spring '05
 R.Metzger
 Functional equation, explicit function

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