MacMahon's Partition Analysis: The Omega Package

George E. Andrews, Peter Paule, Axel Riese

Research output: Contribution to journalArticle

40 Scopus citations

Abstract

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
Volume22
Issue number7
DOIs
StatePublished - Oct 2001

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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