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Unformatted text preview: n th term of at least one of them.) (5) (a) Show that the generating function of { p k ( n ) } ∞ n =0 is x k (1x )(1x 2 ) · · · (1x k ) where p k ( n ) is the number of partitions of n into k terms. (b) Prove p odd ( n ) = p dist ( n ) using generating functions, where p odd ( n ) and p dist ( n ) are the number of partitions of n into odd terms, and distinct terms, respectively. 1 1 This was done in lecture in a diferent way without using generating Functions. When I was a students I hated those exercises when they told me how to do things, and another prooF wouldn’t be accepted. IF you Feel the same way, skip 5b), and do the Following exercise instead: ±ix t ≥ 0. Show that the sequence { p nt ( n ) } ∞ n =0 will eventually become a constant. What is this constant f ( t )? 1...
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This note was uploaded on 01/12/2012 for the course MATH 681 taught by Professor Wildstrom during the Fall '09 term at University of Louisville.
 Fall '09
 WILDSTROM

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