MacMahon's Partition Analysis VIII. Plane partition diamonds

In his famous book "Combinatory Analysis" MacMahon introduced Partition Ana lysis as a computational method for solving combinatorial problems in conne ction with systems of linear diophantine inequalities and equations, Howeve r, MacMahon failed in his attempt to use his method for a satisfactory trea tment of plane partitions. It is the object of this article to show that ne vertheless Partition Analysis is of significant value when treating non-sta ndard 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 packag e developed by the authors has played a fundamental role. (C) 2001 Academic Press.