MacMahon's Partition Analysis VIII. Plane partition diamonds

被引：26

作者：

Andrews, GE ^{[1
]}

Paule, P

Riese, A

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Johannes Kepler Univ Linz, Symbol Computat Res Inst, A-4040 Linz, Austria

来源：

ADVANCES IN APPLIED MATHEMATICS | 2001年 / 27卷 / 2-3期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1006/aama.2001.0733

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2001 Academic Press.

引用

页码：231 / 242

页数：12