Unformatted text preview: (b) Which function has rank 17? ± 2 1 ¶ = 2 ± 3 1 ¶ = ± 3 2 ¶ = 3 ± 4 1 ¶ = ± 4 3 ¶ = 4 ± 4 2 ¶ = 6 ± 5 1 ¶ = 5 ± 5 2 ¶ = ± 5 3 ¶ = 10 ± 6 1 ¶ = 6 ± 6 2 ¶ = 15 ± 6 3 ¶ = 20 3. (10 pts.) Let L ( n, k ) be the number of (ordered) kelement lists that can be formed from the set S = { 1 , 2 , . . . , n } with the restriction that no element of S can appear more than twice in a list . (If I’d said “more than once”, it would have been lists without repeats.) By considering where n appears in a list obtain a recursion of the form L ( n, k ) = aL ( n1 , k ) + bL ( n1 , k1) + cL ( n1 , k2) where a , b and c may be constants or simple functions of k . END OF EXAM...
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 Fall '08
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 Math, Monotonic function, Convex function, 10 pts, strictly decreasing functions

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