MacMahon's Partition Analysis VIII. Plane partition diamonds

George E. Andrews, Peter Paule, Axel Riese

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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 - 2001

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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