Periodic Antisymmetric Matrices counted by Hermitte Numbers

[Gottfried Helms]

Am 03.12.2005 23:08 schrieb wouter meeussen:
> Antisymmetric: Transpose(A)= -A, so zero diagonals
> Periodic: some matrix power = Identity Matrix
> A067994= Hermitte Numbers= 1,0,2,0,12,0,120,0,1680, ...
> 
> Their periods are all 4.
> Strong law of small numbers checked upto n=8.
> Who says this is self-evident?
> 
> W.
> 
> 
> 
> 
> 
A
0    2^0
2    2^1 *1
4    2^2 *1*3
6    2^3 *1*3*5
8    2^4 *1*3*5*7
10   2^5 *1*3*5*7*9 --- but this seems very regular.

What was your expectation about periods=4 ?
Is it something with phi()-function or order of cyclic subgroups?
Then the reason for some irregularity may be, that 9 isn't prime.

Gottfried Helms