MacMahon’s Partition Analysis V: Bijections, Recursions, and Magic Squares

George E. Andrews (), Peter Paule (), Axel Riese () and Volker Strehl ()
Additional contact information
George E. Andrews: The Pennsylvania State University, Department of Mathematics
Peter Paule: Johannes Kepler University Linz, Research Institute for Symbolic Computation
Axel Riese: Johannes Kepler University Linz, Research Institute for Symbolic Computation
Volker Strehl: Friedrich-Alexander-Universität Erlangen-Nürnberg, Computer Science Institute-Informatik 8

A chapter in Algebraic Combinatorics and Applications, 2001, pp 1-39 from Springer

Abstract: Abstract A significant portion of MacMahon’s famous book “Combinatory Analysis” is devoted to the development of “Partition Analysis” as a computational method for solving problems in connection with linear homogeneous diophantine inequalities and equations, respectively. Nevertheless, MacMahon’s ideas have not received due attention with the exception of work by Richard Stanley. A long range object of a series of articles is to change this situation by demonstrating the power of MacMahon’s method in current combinatorial and partition-theoretic research. The renaissance of MacMahon’s technique partly is due to the fact that it is ideally suited for being supplemented by modern computer algebra methods. In this paper we illustrate the use of Partition Analysis and of the corresponding package Omega by focusing on three different aspects of combinatorial work: the construction of bisections (for the Refined Lecture Hall Partition Theorem), exploitation of recursive patterns (for Cayley compositions), and finding nonnegative integer solutions of linear systems of diophantine equations (for magic squares of size 3).

Keywords: Diophantine Equation; Partition Analysis; Bijective Proof; Generate Function Expression; Partial Fraction Decomposition (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59448-9_1

Ordering information: This item can be ordered from
http://www.springer.com/9783642594489

DOI: 10.1007/978-3-642-59448-9_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().