Q. about {0,1}-matrices.
Brendan McKay
bdm at cs.anu.edu.au
Sun Jan 7 00:19:28 CET 2007
In a little less than 30 minutes, my C program counted:
1, 4, 68, 5008, 1603232, 2224232640
The next value would take 1-2 years of cpu time, which is not
out of the question but would take an amount of personal effort
that I can't see justification for at the moment.
Btw, all I did was to extend each robust matrix in all possible
ways and compute its determinant. It is possible that there is
a clever way of avoiding determinant computations for a large
fraction of matrices, in which case it would all get much faster.
Brendan.
* Brendan McKay <bdm at cs.anu.edu.au> [070107 09:35]:
> * Edwin Clark <eclark at math.usf.edu> [070107 09:08]:
> > On Sat, 6 Jan 2007, Ferenc Adorjan wrote:
> >
> > > Hello Neil and Seqfans,
> > >
> > > I have composed a Pari program to determine the number of nxn robust
> > > 0,1 matrices.
> > > Certainly, the program below is neither optimal nor verfied. It
> > > provides properly the value of 4 and 68, but as the fourth term it
> > > gives 5440 instead of the value in your sequence (5008).
> > > Somebody should verify the program (or the term #4) before anybody
> > > tries to calculate the fifth term.
> > > Ferenc
> >
> > I wrote a Maple program to calculate nxn robust matrices. It
> > agrees with the values 1, 4, 68, 5008 given by Neil. It is
> > now using those 5008 of size 4x4 to compute the number of
> > 5x5's. At the present rate it should be done in about 5 more
> > hours.
>
> I did it in C and got 1, 4, 68, 5008, 1603232 in one second.
> Maybe the next one will be done in an hour or so. I expect
> it will be 1-2 billion, and someone should check it.
> a(6) is not impossible but would need a good reason.
>
> Brendan.
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