Need to count restricted partitions? This paper presents Algorithm 448, a subroutine named *COUNT*, designed to efficiently compute the number of distinct partitions of a positive integer *m*, subject to restrictions defined by a *k*-tuple *c*. Given *c* and an integer *n*, *COUNT* computes an array of values representing the number of restricted partitions for all integers from 1 to *n*. Many combinatorial enumeration problems can be expressed in terms of these restricted partition numbers. This algorithm provides a valuable tool for solving various combinatorial problems, including those in number theory and discrete mathematics, with broad applications in fields requiring efficient enumeration techniques.
Published in Communications of the ACM, this article is relevant to the journal’s focus on algorithms and computational methods. The presentation of Algorithm 448 for computing the number of multiply-restricted partitions fits the journal's scope by providing a practical solution to a combinatorial enumeration problem. This is especially relevant for computer scientists and mathematicians.