powers of Antisymmetric Signed binary Matrices

[Edwin Clark]

I get 

    1, 3, 7, 25, 81

for a(n), n=1...5. Where a(n) is the number of antisymmetric n x n
matrices T with entries 0,1,or -1 for which T^k also has entries 0, 1 or
-1 for k from 1 to n^2.

BTW I'm not sure that "signed binary" is a well-known concept. I did,
however, find reference to "signed bit" representation of integers. So if
used, I think it is a good idea to define it.

 --Edwin


On Mon, 25 Aug 2003, Meeussen Wouter (bkarnd) wrote:

> Thanks Edwin,
> 
> exactly the critical feedback I hoped for.
> 
> bonus:
> just a bit extra work to isolate the cases with
> *true* zero diagonals, and I got them both ways.
> 
> maybe analogous for zero trace.
> 
> to what nXn did you get?
> can you communicate your results so far?
> 
> W.
> 
> 
> 
> -----Original Message-----
> From: Edwin Clark [mailto:eclark at math.usf.edu]
> Sent: maandag 25 augustus 2003 18:05
> To: wouter meeussen
> Cc: Seqfan (E-mail)
> Subject: Re: powers of Antisymmetric Signed binary Matrices
> 
> Wouter:
> 
> I was getting different numbers, but then I finally noticed that in your
> definition of antisymmetric you allow arbitrary diagonal elements. Perhaps
> you should call your matrices quasi-antisymmetric or something like
> that?
> 
> The usual definition of antisymmetric is Tij = -Tji for all i,j. This
> means that the diagonal elements should be 0. What you have is of the form
> D + T where D is diagonal and T is antisymmetric.
> 
> Edwin
> 
> 
> 
> ------------------------------------------------------------
>     W. Edwin Clark, Math Dept, University of South Florida,
>            http://www.math.usf.edu/~eclark/
> ------------------------------------------------------------
> 
> 
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------------------------------------------------------------
    W. Edwin Clark, Math Dept, University of South Florida,
           http://www.math.usf.edu/~eclark/
------------------------------------------------------------