%N A052182: Right or Left cyclic permutations?

[Max Alekseyev]

On Mon, Mar 17, 2008 at 10:59 PM, zak seidov <zakseidov at yahoo.com> wrote:
> %N A052182 Determinant of n X n matrix whose rows are
>  cyclic permutations of 1..n.
>  Right or Left cyclic permutations?
>  Clarification needed.
>  E.g., %t A052182 (with RotateLeft) gives opposite
>  signs for n==0,3 (mod 4).

It is easy to see that changing the direction of cyclic rotation
results in multiplication of the matrix determinant by (-1)^[(n-1)/2]
(actually, [(n-1)/2] row swaps are needed to change the matrix from
one direction to the other).
And [(n-1)/2] is odd only for n==0,3 (mod 4).
Therefore, the observed discrepancy in signs seems to be indeed the
result of choosing different direction of cyclic rotations.

Regards,
Max