On a circle we have 2n points (n is a natural nomber). In how many ways we can construct n chords of the circle, which don't intersect each other, joining pairs of the 2n points?
Example: $a_1=1$, $a_2=2$ and $a_3=5$. (There are no 2 chords with a common point (including those 2n points on the circle), so there are exactly n chords)
Counting Problem
Re: Counting Problem
A nice use of Catalan numbers: http://en.wikipedia.org/wiki/Catalan_nu ... binatorics
Exercise: determine how this is bijective with the balanced bracket problem (sixth point in the wiki article).
Exercise: determine how this is bijective with the balanced bracket problem (sixth point in the wiki article).
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Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Re: Counting Problem
So the answer si C(n)! Thank you!