A symmetrical plane partition correspondence |
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Authors: | William H Burge |
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Affiliation: | IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598 USA |
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Abstract: | MacMahon conjectured the form of the generating function for symmetrical plane partitions, and as a special case deduced the following theorem. The set of partitions of a number n whose part magnitude and number of parts are both no greater than m is equinumerous with the set of symmetrical plane partitions of 2n whose part magnitude does not exceed 2 and whose largest axis does not exceed m. This theorem, together with a companion theorem for the symmetrical plane partitions of odd numbers, are proved by establishing 1-1 correspondences between the sets of partitions. |
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