Complete sets of solutions to partition-distribution equations

In the analysis of algebraic equations in discrete statistical systems, it is often necessary to find the complete sets of non-negative integer solutions k1,k2,k3, . . . to the partition–distribution equations: k1 þ k2 þ k3 þ . . . 1⁄4 m and k1þ 2k2 þ 3k3 þ . . . 1⁄4 n. In this paper, two efficient methods, indirect and recurrent, are derived to find the desired results for any given positive integers n and m. An example is provided to demonstrate the merits of these two methods. 2007 Elsevier Inc. All rights reserved.