I tried to understand what you wrote and am left with questions. Take [T=:(0 1 1, 1 0 1, 1 1 0,:1 1 1);0 0 0,0 0 1,0 1 0,:1 0 0 +-----+-----+ |0 1 1|0 0 0| |1 0 1|0 0 1| |1 1 0|0 1 0| |1 1 1|1 0 0| +-----+-----+
With Gloc=: $ #: I.@, from the Journal of J, I get Gloc L:0 (0;1)=L:0 T +---+---+ |0 0|1 2| |1 1|2 1| |2 2|3 0| +---+---+ From this I get (, (>:@$|"1 -.)L:0,:~-.L:0)Gloc L:0 (0;1)=L:0 T +-----+-----+ |0 0 |1 2 | |1 1 |2 1 | |2 2 |3 0 | +-----+-----+ | 1 1| 0 _1| | 0 0|_1 0| |_1 _1|_2 1| +-----+-----+ |1 1 |0 2 | |0 0 |3 0 | |3 2 |2 1 | +-----+-----+ Which are the original locations of 0 and 1 respectively, there negations (-.), and these converted to locations. Being selfdual we should have the first and the reversed latest row to be equal, however (-: [:|. (>:@$|"1 -.)L:0)Gloc L:0 (0;1)=L:0 T 0 What do I do wrong? R.E. Boss > -----Oorspronkelijk bericht----- > Van: Chat <[email protected]> Namens Nollaig > MacKenzie > Verzonden: zondag 18 augustus 2019 06:37 > Aan: [email protected] > Onderwerp: [Jchat] Number of self-dual arrays of rank N; OEIS > > > I was a little dissatisfied with the discussion, in my “A NOTE ON TRUTH- > FUNCTIONAL SELF-DUALITY” in the June 2018 Journal of J, of the number of > self-dual N axis arrays (N= 0,1,2,….). A succinct statement is: The number of > self-dual arrays of N axes = the number of non-self-dual non-degenerate > arrays of N-1 axes. > > This follows from the fact that the {. and {: of a rank N self-dual must be > duals, one of the other. So each of the nondegenerate N -1 rank arrays gives > rise to a rank N self-dual, except for the N-1 rank self-duals, which if > laminated with their duals would yield an N rank array with {. and {: > identical. > > I use “laminate” a little idiosyncratically here. I mean > > lam=: ,`,:@.(0<#@$@]) > > To illustrate: There are 2 non-self-dual non-degenerate arrays for N=0, > namely scalar 0 and 1. > > So there will be 2 self-dual arrays for N=1, namely > > 0 lam 1 1 lam 0 > > Thus there are 0 non-self-dual nondegenerate arrays of rank 1, and > therefore no self-duals of rank 2. > > There are 10 non-self-dual non-degenerate arrays of rank 2, and therefore > 10 self-duals of rank 3. > > The sequence is: 0,2,0,10,208…. > > By this reasoning the next term (for N=5) should be 64386. I went to OEIS.org > to check, and found that 0,2,0,10,208 wasn’t listed. > > I’m tempted to submit the sequence to OEIS, but I don’t have an elegant > formula for generating it, and I don’t know whether it is of any significance. > As a non-mathematician I don’t want to make a fool of myself. > > Any mathematical types here have advice (other than “nothing wrong with > making a fool of yourself”)? > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
