finalw04 - Math 239 Winter 2004 1 1(a Let k be a given...

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Math 239 Winter 2004 1 1. (a) Let k be a given positive integer. Find the generating function for the number of com- positions of n having k parts, where each part is an odd positive integer. (b) [6 marks] Find the generating function for the number of compositions of n with an odd number of parts, where each part is congruent to 2 (mod 4).
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Math 239 Winter 2004 2 2. (a) [3 marks] Write down a decomposition that uniquely creates the set of binary strings in which every block of 0’s has odd length and every block of 1’s has length greater than 2. (b) [3 marks] Write down a decomposition that uniquely creates the set of binary strings that do not contain the substring 111000.
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Math 239 Winter 2004 3 3. [8 marks] As usual, let the weight of a binary string be its length. Determine the generating function for the set of binary strings in which a block of 1’s is never followed by a block of 0’s of the same length.
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Math 239 Winter 2004 4 4. (a) [2 marks] Define a bridge in a graph.
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