Q. about {0,1}-matrices.

[Brendan McKay]

* Brendan McKay <bdm at cs.anu.edu.au> [070107 11:27]:
> Incidentally, the definition of A006383 (Number of equivalence
> classes of n X n binary matrices when S_n acts independently on the
> rows and columns) seems to be the same as the definition of A002724
> (Number of inequivalent n X n binary matrices, where equivalence
> means permutations of rows and/or columns) but the numbers are
> different - what gives?  A002724 is the one that seems to have
> values fitting the definition.


To answer my own question: A006383 also allows the operation of
complementing columns (but, apparently, not rows).  Neil, can
you fix that?

Brendan.
 
 
> * N. J. A. Sloane <njas at research.att.com> [070107 10:50]:
> > Brendan said:
> > 
> > In a little less than 30 minutes, my C program counted:
> > 
> >    1, 4, 68, 5008, 1603232, 2224232640
> > 
> > Me:  Pretty amazing!   
> > 
> > Did your C program use the following observation:
> >     - the number of ways to add a border to an n-1 X n-1
> >       matrix A doesn'y change if you permute the rows
> >       and columns of A
> > 
> > For going from n=6 to n=7 that's a potential saving
> > of 6! * 6!.  In other words, for each of the 2224232640
> > 6x6s, put it into canonical form.
> > When you have all the canon. forms, and their multiplicities,
> > then see how many ways each can be extended.
> > But you are the Latin square expert, so probably you did this
> > without thinking it was worth mentioning.
> > 
> > Neil