powers of Antisymmetric Signed binary Matrices

[wouter meeussen]

point(s) taken,

it's becoming:
"invertable (-1,0,1) nXn matrices having (Tij = -Tji ;i<j) such that all T^k (k= 1..12) are also
(-1,0,1) matrices"

and comment:
"the matrix powers T^k reach identity I for k a divisor of 12. All are both invertible (non-zero
determinant) (-1,0,1)-matrices and "pseudo-anti-symmetric" (that is Tij=-Tji except for the main
diagonal, or, equivalently, the sum of an anti-symmetric and a diagonal matrix)."

I guess the comment could be shorter, but the little bit extra is nice for the bibliographically
challenged like me. Beg pardon. ;-))

This feels definitely groupy but can't put my digit on it.
The magic "12" (was a cautious n^2) must point to rotations & reflections of the inherently square
soul of the matrix, no?

fumblingly yours,

W.

PS. keywords: should I call them "mult" ??

----- Original Message -----
From: "Marc LeBrun" <mlb at fxpt.com>
To: <Seqfan at ext.jussieu.fr>
Sent: Monday, August 25, 2003 11:14 PM
Subject: RE: powers of Antisymmetric Signed binary Matrices


> > Edwin Clark
>  > ...with entries 0,1,or -1 ...
>  > BTW I'm not sure that "signed binary" is a well-known concept. I did,
>  > however, find reference to "signed bit" representation of integers.
>
> Knuth calls the number system with "trits" -1, 0, +1 "balanced ternary".
>
> But in this context "binary" or "ternary" seems misleading, since here
> these values are actual magnitudes, not the components of a representation.
>
> Why not just say something like
>
>    "Number of nXn matrices whose k-th powers for 0<=k<=n^2 have all
> elements in {0,1}"
>
> or "...{-1,0,+1}" as the case may be?
>
> Writing these sets out explicitly is actually more concise than the "-ary"
> jargon anyway!
>
> Perhaps I missed this: what's the significance of the n^2?
>
> Thanks!
>
>
>
>