Vol. 92, No. 2, 1981

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Matrix correspondences of plane partitions

Emden Robert Gansner

Vol. 92 (1981), No. 2, 295–315

Three correspondences between nonnegative integer arrays and plane partitions, due to Burge, Knuth, and Hillman and Grassl, are investigated. A variety of parallel and complementary properties are derived for the first two. In particular, the images of an array under the correspondences are characterized in terms of certain sets of “paths” in the arrays. The correspondences are also related to each other through the action of the dihedral group on rectangular arrays. Finally, the Hillman-Grassl correspondence is similarly characterized in terms of sets of paths and is shown to be an extension of Burge’s correspondence.

Mathematical Subject Classification 2000
Primary: 05A17
Secondary: 05A05, 05A15, 20B25
Received: 8 August 1979
Revised: 26 June 1980
Published: 1 February 1981
Emden Robert Gansner