@article{d02de5ec132d4fe1805cae3fb4fc89ca,
title = "MacMahon's Partition Analysis VIII. Plane partition diamonds",
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.",
author = "Andrews, \{George E.\} and Peter Paule and Axel Riese",
note = "Funding Information: 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. 2001 Elsevier Science 1Partially supported by NSF Grant DMS-9206993. 2Supported by SFB Grant F1305 of the Austrian FWF.",
year = "2001",
doi = "10.1006/aama.2001.0733",
language = "English (US)",
volume = "27",
pages = "231--242",
journal = "Advances in Applied Mathematics",
issn = "0196-8858",
publisher = "Academic Press Inc.",
number = "2-3",
}