Colin Mallows's problems

[N. J. A. Sloane]

Mitch says:

> >  For each m,n, how many of these arrangments can be realised as the ordering 
> >of numbers of the form x_i + y_j?
> 
> Is there an example for this? I don't understand how this is supposed to 
> work.


Me:  i assumed it was something like this:   certain of
these arrangements can be obtained by taking m numbers x1 ... xm
in increasing order of course
and n numbers y1 ... yn, and filling the array with M_{i,j} = xi + yj.

If we are lucky, this will use all the numbers 1 ... mn exactly once
- in how many ways can this be done?

NJAS