March 30 Exercise (b) and (c) from lecture

Posted on March 30, 2016 by Kate Poirier

Exercise: Complete parts (b) and (c) below for your team.

Team parentheses:
Let C_n be the number of ways of parenthesizing a product of n+1 numbers.

Team binary rooted trees:
Let C_n be the number of full, binary, rooted trees with n+1 leaves.

Team triangulated polygons:
Let C_n be the number of ways of triangulating a polygon with n+2 sides.

(b) Find a recursive formula for C_n. (That is, find a formula for C_n in terms of C_0, C_1, C_2, \dots, C_{n-1}.)

(c) Use your formula from (b) to determine C_5 and C_6.

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