a3 - MATH 239 Assignment 3 This assignment is due at noon...

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MATH 239 Assignment 3 This assignment is due at noon on Friday, June 8, 2007, in the drop boxes opposite the Tutorial Centre, MC 4067. 1. (a) Determine a generating function for the compositions of n in which all parts are odd. As usual, the weight of a composition is the sum of its parts. (b) Determine a generating function for the of compositions of n in which at least one part is even. (c) Let the number of compositions of n with at least one even part be b n . Determine a recurrence relation for the b n ’s, and sufficient initial conditions to uniquely define the terms of the sequence { b n } . Evaluate b 10 . 2. (a) Let A = { 10 , 101 } and let B = { 001 , 100 , 1001 } . For each of the sets AB and BA , de- termine whether or not the elements are uniquely created. Find the generating function for AB and BA with respect to length. (b) Let A = { 00 , 101 , 11 } and B = { 00 , 001 , 10 , 110 } . Prove that the elements of A * are uniquely created, but the strings of B * are not. Find the generating function for
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