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A General Algorithm for the MacMahon Omega Operator.
- Source :
- Annals of Combinatorics; 2003, Vol. 7 Issue 4, p467-480, 14p
- Publication Year :
- 2003
-
Abstract
- In his famous book “Combinatory Analysis” MacMahon introduced Partition Analysis (“Omega Calculus”) as a computational method for solving problems in connection with linear diophantine inequalities and equations. The technique has recently been given a new life by G.E. Andrews and his coauthors, who had the idea of marrying it with the tools of to-day’s Computer Algebra. The theory consists of evaluating a certain type of rational function of the form A(λ)<superscript>-1</superscript>B(1/λ)<superscript>-1</superscript> by the MacMahon Ω operator. So far, the case where the two polynomials A and B are factorized as products of polynomials with two terms has been studied in details. In this paper we study the case of arbitrary polynomials A and B. We obtain an algorithm for evaluating the Ω operator using the coefficients of those polynomials without knowing their roots. Since the program efficiency is a persisting problem in several-variable polynomial Calculus, we did our best to make the algorithm as fast as possible. As an application, we derive new combinatorial identities. [ABSTRACT FROM AUTHOR]
- Subjects :
- ALGORITHMS
PARTITIONS (Mathematics)
DIOPHANTINE equations
COMBINATORICS
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 02180006
- Volume :
- 7
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Annals of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 13044914
- Full Text :
- https://doi.org/10.1007/s00026-003-0197-8