MacMahon's Partition Analysis

The Omega Package

George E. Andrews, Peter Paule, Axel Riese

Research output: Contribution to journalArticle

35 Citations (Scopus)

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 - Jan 1 2001

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Computer Algebra
Partition
Calculus
Diophantine Inequalities
Diophantine equation
Computational Methods
Object

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Cite this

Andrews, George E. ; Paule, Peter ; Riese, Axel. / MacMahon's Partition Analysis : The Omega Package. In: European Journal of Combinatorics. 2001 ; Vol. 22, No. 7. pp. 887-904.
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MacMahon's Partition Analysis : The Omega Package. / Andrews, George E.; Paule, Peter; Riese, Axel.

In: European Journal of Combinatorics, Vol. 22, No. 7, 01.01.2001, p. 887-904.

Research output: Contribution to journalArticle

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