METU Department of Mathematics Math 405 Combinatorics Spring 2010

QUIZ 5

Problem 1. Calculate the Catalan number c_{5}. Problem 2. Give a list of all Dyck words of length 5 + 5. Connect 10 points on a circle with 5 non-intersecting chords in accord with these Dyck’s words. Problem 3. Sketch the corresponding binary tree, and triangulate a polygon in accord with the product (ab)((cd)e) (mark the base of this polygon).