MacMahon's Partition Analysis VIII. Plane partition diamonds

George E. Andrews, Peter Paule, Axel Riese

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In his famous book "Combinatory Analysis" MacMahon introduced Partition Analysis as a computational method for solving combinatorial problems in connection with systems of linear diophantine inequalities and equations. However, MacMahon failed in his attempt to use his method for a satisfactory treatment of plane partitions. It is the object of this article to show that nevertheless Partition Analysis is of significant value when treating non-standard types of plane partitions. To this end "plane partition diamonds" are introduced. Applying Partition Analysis a simple closed form for the full generating function is derived. In the discovering process the Omega package developed by the authors has played a fundamental role.

Original languageEnglish (US)
Pages (from-to)231-242
Number of pages12
JournalAdvances in Applied Mathematics
Volume27
Issue number2-3
DOIs
StatePublished - Jan 1 2001

Fingerprint

Plane Partitions
Computational methods
Strombus or kite or diamond
Diamonds
Partition
Diophantine Inequalities
Diophantine equation
Combinatorial Problems
Computational Methods
Generating Function
Linear Inequalities
Linear equation
Closed-form

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

Andrews, George E. ; Paule, Peter ; Riese, Axel. / MacMahon's Partition Analysis VIII. Plane partition diamonds. In: Advances in Applied Mathematics. 2001 ; Vol. 27, No. 2-3. pp. 231-242.
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MacMahon's Partition Analysis VIII. Plane partition diamonds. / Andrews, George E.; Paule, Peter; Riese, Axel.

In: Advances in Applied Mathematics, Vol. 27, No. 2-3, 01.01.2001, p. 231-242.

Research output: Contribution to journalArticle

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