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We present a simple bijection between permutation matrices and descendingplane partitions without special parts. This bijection is already mentioned inwork of P. Lalonde (without giving the details); it involves the inversionwords of permutations and the (well-known) representation of descending planepartitions as families of non--intersecting lattice paths. (Taking a shortdetour, we will also exhibit how the (well--known) enumeration of descendingplane partitions follows easily from the evaluation of Andrew's determinant.)

A simple bijection between permutation matrices and descending plane partitions without special parts