论文信息 - MacMahon's Partition Analysis: The Omega Package

MacMahon's Partition Analysis: The Omega Package

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

[1] George E. Andrews,et al. MacMahon’s Partition Analysis: I. The Lecture Hall Partition Theorem , 1998 .

[2] D. Gouyou-Beauchamps. Lecture Hall Partitions , 1997 .

[3] G. Andrews,et al. MacMahon’s Partition Analysis V: Bijections, Recursions, and Magic Squares , 2001 .

[4] W. E. H. B.,et al. Aufgaben und Lehrsätze aus der Analysis. , 1925, Nature.

[5] P. A. Macmahon. Memoir on the Theory of the Partition of Numbers. Part I , 2022 .

[6] George E. Andrews,et al. MacMahon's Partition Analysis: II Fundamental Theorems , 2000 .

[7] P. A. Macmahon. IX. Memoir on the theory of the partitions of numbers. - Part VI. Partitions in two-dimensional space, to which is added an adumbration of the theory of the partitions in three-dimensional space , 2022 .

[8] Emil Grosswald,et al. The Theory of Partitions , 1984 .

[9] G. Pólya,et al. Aufgaben und Lehrsätze aus der Analysis , 1926, Mathematical Gazette.

[10] Anton Betten,et al. Algebraic Combinatorics and Applications : Proceedings , 2001 .