# n-gon sequence

Jon Perry perry at globalnet.co.uk
Mon Oct 14 19:15:12 CEST 2002

```With further research, I got 20 intersections from 3 triangles - I did say
it was without proof, as is my 20 being maximal.

(Create a Star of David, and connect 2 opposite vertices up. The number of
intersections here is 4).

I also got the sequence for maximal intersections of 2 n-gons wrong.

3 and 4 are 6,8, but I got 18 and 20 intersection from two (non-self
intersecting) 5- and 6- gons.

But again these are without proof, so the bound might rise again.

Jon Perry
perry at globalnet.co.uk
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
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-----Original Message-----
From: Brendan McKay [mailto:bdm at cs.anu.edu.au]
Sent: 13 October 2002 14:53
Cc: Seqfan at Ext.Jussieu.Fr
Subject: Re: n-gon sequence

* Jon Perry <perry at globalnet.co.uk> [021013 23:02]:
> Is this sequence known? I've only worked out the first 2 terms of each.
>
> The maximum number of intersections of k n-gons.
>
> e.g. with triangles, the sequence opens 0,6 - my next term is 16, but this
> is without proof.
>
> For the general n-gon, the sequence always opens 0,2n

Can you give a more precise definition please?  It is easy to
draw 3 triangles so that each pair intersect in 6 points and
all intersections are distinct, making 18 altogether.  So I
guess you must mean something else.

Brendan.

```