On asymptotic properties of a number theoretic function arising out of a spin chain model in statistical mechanics

摘要

Let A = [(1)(0)(1)(1)] and B = [(1)(1)(0)(1)] Let N be a positive integer and define Phi (N) as the number of matrices, C, which are products of A and B, where both A and B must occur, such that the trace, Tr(C) = N. It has been conjectured that Phi (N) similar to N log N (N --> infinity), see [10]. In this note we consider the summatory function Psi (N) = Sigma (n less than or equal toN) Phi (n) and show that Psi (N) similar to 6/pi (2) N-2 log N (N --> infinity). [References: 19]