total no. of different complete line sequences that can be drawn using n points in a circle?

Question

we are given n points, 1 to n which are placed on a circle. we need to draw lines b/w the points. one point can only be a part of one line. we need to draw lines in such a way that no two lines intersect. one complete line sequence is called if all the points are used to draw the line segments. how can I find total no. of different complete line sequences that can be drawn using n points in a circle?

for ex: if points on a circle is 6 then there could be max. 5 complete line sequences.

Any formula which can be derived for this problem?

I would suggest, find the answer for 2 points, then for 3, then 4, and so on, until maybe you see a pattern, and maybe can prove the pattern continues. — Gerry Myerson, Apr 03 '16 at 07:21
That's a good start. Do a few more. I bet it's the Catalan numbers. https://oeis.org/A000108 — Gerry Myerson, Apr 03 '16 at 07:28
@GerryMyerson Your OEIS entry (the link) contains the comment ___Ways of joining 2n points on a circle to form n nonintersecting chords.___ so it is a pretty safe bet. Good reference. — Jeppe Stig Nielsen, Apr 03 '16 at 09:27

score 2 · Answer 1 · edited Apr 13 '17 at 12:20

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Number of ways to pair off $2n$ points such that no chords intersect Is it the same question ?

If yes, then Catalan numbers is the answer(as mentioned in the post)

Edit: If you read the problem, its not directly related. N=3 in the redirected post is equivalent to N=6 in this post. Catalan numbers is followed for the even numbers, for odd answer is 0.

edited Apr 13 '17 at 12:20

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answered Apr 03 '16 at 08:10

foobaraccount

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total no. of different complete line sequences that can be drawn using n points in a circle?

1 Answers1