1. A General Algorithm for the MacMahon Omega Operator.
- Author
-
Han, Guo-Niu
- Subjects
ALGORITHMS ,PARTITIONS (Mathematics) ,DIOPHANTINE equations ,COMBINATORICS ,MATHEMATICS - 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)
-1 B(1/λ)-1 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]- Published
- 2003
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