[An Infinite 2-Dimensional Derangement]

[Christian G. Bower]

Leroy Quet <qq-quet at mindspring.com> wrote:

> Take an infinite matrix where each positive integer occurs exactly once 
> in each column and in each row.
[snip]
> 1, 2, 3, 4, 5, 6, 7, 8...
> 2, 1, 4, 3, 6, 5, 8, 7...
> 3, 4, 1, 2, 7, 8, 5, 6...
> 4, 3, 2, 1, 8, 7, 6, 5...
> 5, 6, 7, 8, 1, 2, 3, 4...
> 6, 5, 8, 7, 2, 1, 4, 3...
> 7, 8, 5, 6, 3, 4, 1, 2...
> 8, 7, 6, 5, 4, 3, 2, 1...
[snip]
> So, the most general question I will ask is, what is a closed-form way
> to calculate each element given only its row and column?

((a-1) XOR (b-1)) + 1

See A003987

Christian