Colin Mallows's problems

[Mitchell Harris]

On Fri, 10 Jun 2005, N. J. A. Sloane wrote:

>My former colleague Colin Mallows sent me this:
>
>   You asked for problems.     I would very much like to know the answers 
>to the following two; they may have been done by someone, but I don't 
>think they are in the OEIS.
>
>  A039622 gives the number of ways of filling an nxn matrix with the integers 
>1:n^2 so that each row and column is in increasing order.    What about a 
>mxn matrix?     (for 2xn we get the Catalan numbers).

A060854 ...number of ways to arrange the numbers 1,2,..,m*n in an m X n 
           matrix so that each row and each column is increasing.

>  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.

-- 
Mitch Harris