Re: The set of necessary FISONs

On 15.02.2025 20:41, Jim Burns wrote:

On 2/15/2025 7:56 AM, WM wrote:

 

swaps such that, after all swaps,
Bob is not anywhere he has swapped to.

>
Then your logic allows
lossless exchanges with losses.
Not acceptable.

>
If you accept ST+F

 I don't.

The set of rows, the set of columns, and ⋃{F}
do not change.

>
Then it would need to contain ℕ,
as an infinite FISON.

>
Infinite FISONs
(finite initial segments of naturals)
are not acceptable.

 Correct. Therefore the figure
{1}
{2, 1}
{3, 2, 1}
...
is finitely broad and finitely high.
 Regards, WM