User blog comment:DrCeasium/new hyperfactorial array notation/@comment-5150073-20130415141127/@comment-7484840-20130415165548

As far as I am aware, the only reason that the definition of BEAF would change by changing the layout of an array (if the same number of entries were kept with the same value and order) is if where rows begin and end was changed, due to the definition of the copilot as not existing if the pilot is at the beginning of a row. Changing 3*2 & 3 to 6&3 does change this, but, removing higher exponents has no effect on rows.

For example, a dulatri, 3^(2*3) & 3, (the one with the picture displayed on Bowers' website)  would evaluate to 3^6, and in terms of row beginnings and endings this is exactly the same as 3^3 & 3^3 & 3, or 3^(2*3) & 3. However, evaluating 3^6 to 729 would change the row beginnings and endings. This must be true because 3^6 = 3^(2*3), and in both of these the rows are of length 3, so there must be the same amount, and so therefore, must be equal. Unless, of course, I have just horribly misunderstood how BEAF works. So as far as I know, 3^3^3^3 can be simplified down to  3^762559749487 for the same reason that 3*2 & 3 = {3,3,3 (1) 3,3,3} can't be simplified to 6 & 3 = {3,3,3,3,3,3}, that is, changing the rows.

That aside, what did you think of my notation and numbers?