Counting Problem

For discussing Olympiad Level Combinatorics problems
yo79
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Counting Problem

Unread post by yo79 » Sat Feb 23, 2013 7:27 pm

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)

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*Mahi*
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Re: Counting Problem

Unread post by *Mahi* » Sat Feb 23, 2013 10:27 pm

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).
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yo79
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Re: Counting Problem

Unread post by yo79 » Sun Feb 24, 2013 2:56 am

So the answer si C(n)! Thank you!

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