Partition Analysis Xii: Plane Partitions
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Macmahon’s Partition Analysis Xii: Plane Partitions
MacMahon developed partition analysis as a calculational and analytic method to produce the generating function 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 our retrieval of MacMahon’s original project. One of the key results obtained with partition analysis...
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In the present study, natural convective heat transfer in a partitioned square cavity utilizing nanofluids is studied. The vertical left and right walls are considered as the hot and cold walls, respectively and the partitions assumed to be adiabatic. The nanofluid used in this study is Al2O3 with the volume fraction of 20%. It is assumed that nanofluid is a single phase f...
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We define three combinatorial models for b sln crystals, parametrized by partitions, configurations of beads on an “abacus”, and cylindric plane partitions, respectively. These are reducible, but we can identify an irreducible subcrystal corresponding to any dominant integral highest weight Λ. Cylindric plane partitions actually parametrize a basis for VΛ ⊗ F , where F is the space spanned by p...
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In this paper we continue the partition explorations made possible by Omega, the computer algebra implementation of MacMahon’s Partition Analysis. The focus of our work has been partitions associated with directed graphs. The graphs considered here are made up of chains of hexagons, and the related generating functions are infinite products. Somewhat unexpectedly, while the generating functions...
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تاریخ انتشار 2006