MacMahon's Partition Analysis XII: Plane Partitions

Peter Paule; George E. Andrews

doi:10.1112/jlms/jdm079

MacMahon's Partition Analysis XII: Plane Partitions

Peter Paule, George E. Andrews

Research Institute for Symbolic Computation

Research output: Contribution to journal › Article › peer-review

Abstract

MacMahon developed Partition Analysis as a calculational and analytic method to produce the generating functions for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of MacMahon's original project. One of the key results obtained with Partition Analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.

Original language	English
Pages (from-to)	647-666
Number of pages	20
Journal	Journal of the London Mathematical Society
Volume	76
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jdm079
Publication status	Published - Dec 2007

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

Access to Document

10.1112/jlms/jdm079

Cite this

@article{a96a4ae23f4449769bf9964269b8a5fb,

title = "MacMahon's Partition Analysis XII: Plane Partitions",

abstract = "MacMahon developed Partition Analysis as a calculational and analytic method to produce the generating functions for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of MacMahon's original project. One of the key results obtained with Partition Analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.",

author = "Peter Paule and Andrews, \{George E.\}",

year = "2007",

month = dec,

doi = "10.1112/jlms/jdm079",

language = "English",

volume = "76",

pages = "647--666",

journal = "Journal of the London Mathematical Society",

issn = "1469-7750",

publisher = "London Mathematical Society",

number = "3",

}

TY - JOUR

T1 - MacMahon's Partition Analysis XII: Plane Partitions

AU - Paule, Peter

AU - Andrews, George E.

PY - 2007/12

Y1 - 2007/12

N2 - MacMahon developed Partition Analysis as a calculational and analytic method to produce the generating functions for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of MacMahon's original project. One of the key results obtained with Partition Analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.

AB - MacMahon developed Partition Analysis as a calculational and analytic method to produce the generating functions for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of MacMahon's original project. One of the key results obtained with Partition Analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.

UR - https://www.scopus.com/pages/publications/44649160673

U2 - 10.1112/jlms/jdm079

DO - 10.1112/jlms/jdm079

M3 - Article

SN - 1469-7750

VL - 76

SP - 647

EP - 666

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -

MacMahon's Partition Analysis XII: Plane Partitions

Abstract

Fields of science

Access to Document

Other files and links

Cite this