MacMahon's Partition Analysis: The Omega Package

George E. Andrews, Peter Paule, Axel Riese

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


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 package Omega. In addition to an introduction to basic facts of 'Omega Calculus', we present a number of applications that illustrate the usage of the package.

Original languageEnglish (US)
Pages (from-to)887-904
Number of pages18
JournalEuropean Journal of Combinatorics
Issue number7
StatePublished - Oct 2001

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'MacMahon's Partition Analysis: The Omega Package'. Together they form a unique fingerprint.

Cite this