Report Number: CS-TR-73-354
Institution: Stanford University, Department of Computer Science
Title: The number of SDR's in certain regular systems.
Author: Klarner, David A.
Date: April 1973
Abstract: Let ($a_1$,...,$a_k$) = $\bar{a}$ denote a vector of numbers, and let C($\bar{a}$,n) denote the n $\times$ n cyclic matrix having ($a_1$,...,$a_k$,0,...,0) as its first row. It is shown that the sequences (det C($\bar{a}$,n): n = k,k+1,...) and (per C($\bar{a}$,n): n = k,k+1,...) satisfy linear homogeneous difference equations with constant coefficients. The permanent, per C, of a matrix C is defined like the determinant except that one forgets about ${(-1)}^{sign \pi}$ where $\pi$ is a permutation.
http://i.stanford.edu/pub/cstr/reports/cs/tr/73/354/CS-TR-73-354.pdf