# Nov11 - Any questions about the exam? Homework? Maple?...

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Homework? Maple? Final exam vs. final project Return exam Give overall comments: 1. Read everything before you start. Some of you didn't realize that when I ask for a formula for a sequence, I want a closed form formula, not a recurrence relation! But I explained this at on the last page of the exam. 2. Show work 3. Check work 4. Using Maple 5. Don't write -1/(x-1) just because Maple does! Final answers should be in simplest, most helpful form Describe breakdown of grades: 100, 97, 96, 91, 85, 68, 67, 66 TODAY: Catalan numbers and parenthesizations of products Catalan numbers and triangulations of polygons The “short” recurrence for Catalan numbers Parenthesizations of products Let P_n be the number of ways to parenthesize a product of n things. E.g., P_1 = P_2 = 1, but P_3 = 2 (since abc can be parenthesized as either (ab)c or a(bc). Claim: For n 3, P_n = P_2 P_{n-2} + P_3 P_{n-3} + … + P{n-2} P_2. This should remind you of … the recurrence relation for Catalan

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## This note was uploaded on 02/13/2012 for the course MATH 491 taught by Professor Propp during the Fall '08 term at UMass Lowell.

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Nov11 - Any questions about the exam? Homework? Maple?...

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