quizfnloc808

# quizfnloc808 - Page 1 Name: MATH 239 QUIZ October 8, 2008...

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Page 1 Name: MATH 239 QUIZ October 8, 2008 Surname: ± D. Jao LEC 001 ± I. Goulden LEC 002 Signature: ± K. Purbhoo LEC 003 ± R. Christian LEC 004 Id.#: Question Value Mark Awarded 1 4 2 6 3 6 4 4 Total 20 Instructions: 1. Please check the box beside your lecture section. 2. The quiz has 5 pages. Put your name at the top of every page of the quiz. 3. Non-programmable calculator allowed, no other aids. 4. If your solution doesn’t ﬁt in the space provided, please continue on the back of the page. 1

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Page 2 Name: 1. [4 marks] Let Φ S ( x ) be the generating function for the set S with respect to the weight function w 1 . Let T be a ﬁnite set and let w 2 be a weight function on S × T , given by w 2 ( σ, τ ) = w 1 ( σ ). Show that the generating function for S × T with respect to w 2 is given by | T | · Φ S ( x ). 2
Page 3 Name: 2. (a) [3 marks] For a ﬁxed positive integer k , let a n be the number of solutions to t 1 + . . . + t 2 k = n, where t 1 , t 2 , . . . , t k are even positive integers and

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## This note was uploaded on 07/28/2009 for the course MATH math 239 taught by Professor .... during the Spring '08 term at Waterloo.

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quizfnloc808 - Page 1 Name: MATH 239 QUIZ October 8, 2008...

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