We modify Schutzenberger's ''jeu de taquin'' and Knuth's generalization DELETE of the Robinson Schensted correspondence to apply to unrestricted rather than just column-strict plane partitions. The ''jeu de taquin,'' DELETE, their modifications and the Hillman Grassl mapping are essentially equivalent. We extend the combinatorial methods of Bender and Knuth to give an extension of an elegant unpublished result of Stanley. Our main result is equivalent to the evaluation of a the generating function for column-strict plane partitions of fixed shape with parts less than or equal to m. We prove MacMahon's ''box'' theorem and give a generating function for plane partitions with parts less than or equal to m and the parts below row r form a column-strict plane partition with at most c columns. (C) 1997 Academic Press
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机译：我们修改了Schutzenberger的“ jeu de taquin”和Robin的Schensted对应关系的Knuth的广义DELETE，以应用于不受限制的区域，而不仅仅是列限制的平面分区。 “ jeu de taquin”，“ DELETE”，它们的修改和Hillman Grassl映射在本质上是等效的。我们扩展了Bender和Knuth的组合方法，以扩展Stanley尚未发表的优雅成果。我们的主要结果等同于对部分小于或等于m的固定形状的柱状严格平面分区的生成函数进行评估。我们证明了MacMahon的“盒”定理，并为部分小于或等于m的平面分区提供了一个生成函数，并且在r行以下的部分形成了一个最多c列的列严格平面分区。 （C）1997年学术出版社
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