A Fast Algorithm for MacMahon's Partition Analysis

Macmahon's Partition Analysis Xi: the Search for Modular Forms

MacMahon's Partition Analysis: The Omega Package

In his famous book “Combinatory Analysis” MacMahon introduced Partition Analysis (“Omega Calculus”) as a computational method for solving problems in connection with linear homogeneous diophantine inequalities and equations. The object of this paper is to show that partition analysis is ideally suited for being implemented in computer algebra. To this end we have developed the computer algebra ...

ON RECENT CONGRUENCE RESULTS OF ANDREWS AND PAULE FOR BROKEN ifc-DIAMONDS

In one of their most recent works, George Andrews and Peter Paule continue their study of partition functions via MacMahon's Partition Analysis by considering partition functions associated with directed graphs which consist of chains of hexagons. In the process, they prove a congruence related to one of these partition functions and conjecture a number of similar congruence results. Our first ...

A partition-based algorithm for clustering large-scale software systems

Clustering techniques are used to extract the structure of software for understanding, maintaining, and refactoring. In the literature, most of the proposed approaches for software clustering are divided into hierarchical algorithms and search-based techniques. In the former, clustering is a process of merging (splitting) similar (non-similar) clusters. These techniques suffered from the drawba...

A simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three...