Colin Mallows's problems
Mitchell Harris
harris at tcs.inf.tu-dresden.de
Fri Jun 10 16:49:18 CEST 2005
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
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