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We present a direct bijection between descending plane partitions with nospecial parts and permutation matrices. This bijection has the desirableproperty that the number of parts of the descending plane partition correspondsto the inversion number of the permutation. Additionally, the number of maximumparts in the descending plane partition corresponds to the position of the onein the last column of the permutation matrix. We also discuss the possibleextension of this approach to finding a bijection between descending planepartitions and alternating sign matrices.

A direct bijection between descending plane partitions with no special parts and permutation matrices