||This article may be too technical for most readers to understand. (August 2012)|
||This article needs attention from an expert in mathematics. (March 2013)|
If the given directed graph with boundary is rotation invariant then its hitting matrix is diagonal in Fourier coordinates. Let
be the N'th root of unity or any other root of unity not equal to 1.
We consider the following symmetric Vandermonde matrix:
The square of the Fourier transform is the flip permutation matrix:
The fourth power of the Fourier transform is the identity:
Exercise: Proof that for any :