A2b - k 1 t k c k,n ( q ) , so c k,n ( q ) = t k F n ( t, q...

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DUE FRIDAY, 8 OCTOBER AT 10:31PM This assignment is about partitions. The questions are taken from the Exercises of Section 2.4 (page 38) of the Course Notes. A (15 points) Question 2. B (15 points) Question 3. C (15 points) Question 6. D (15 points) Question 8. E (15 points) Let q and t be indeterminates, and let F n ( t, q ) = Q n i =0 ( 1 - tq i ) - 1 . This has a power series expansion of the form F n ( t, q ) = 1+
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Unformatted text preview: k 1 t k c k,n ( q ) , so c k,n ( q ) = t k F n ( t, q ) . The problem is to determine this coecient. By considering an expression for F n ( tq, q ) that involves F n ( t, q ) , prove that c k,n ( q ) = k Y i =1 ( 1-q n + i )( 1-q i )-1 . F Bonus : (15 points) Find a natural bijection that accounts of the result given in Question A. 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.

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