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Unformatted text preview: 1 with respect to w . Express each generating function (except in (d)) as a rational function , that is, in the form p ( x ) q ( x ) where p ( x ) and q ( x ) are polynomials in x . (In part (d) you may leave your answer as a sum of rational functions.) (a) The set of positive integers that are divisible by 6. (b) The set of positive integers that are congruent to 1 (mod 20). (c) The set of positive integers that are divisible by 4. (d) The set of positive integers that are not divisible by 6 and are not congruent to 1 (mod 20). (e) The set of positive integers that are not divisible by 6 and not divisible by 4. 4. Find the number of compositions of n with k parts, where k 1, in which each part is at least 2 and at most 8....
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 Spring '10
 GUENIN

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