a new problem related to partitions, dissections and polyominoes

[Max]

On 2/22/06, Brendan McKay <bdm at cs.anu.edu.au> wrote:
> Is the following true?
>
> Choose two points, draw a line through them, move it a tiny bit to
> the right if they are vertically above one another or a tiny bit
> upwards otherwise, then that gives all cases.  Upper bound
> binomial(n^2,2) which seems pretty good.  I proved nothing!

Brendan,

If I got you correctly, you describe so-called "stable" threshold
functions. But there are also "unstable" ones. Please refer to my
paper for precise definitions and formulas
http://arxiv.org/abs/math.CO/0602511

Max