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We present a bijection between permutation matrices and descending planepartitions without special parts, which respects the quadruple of statisticsconsidered by Behrend, Di Francesco and Zinn--Justin. This bijection involvesthe inversion words of permutations and the "usual" representation ofdescending plane partitions as families of non--intersec\-ting lattice paths.

A bijection between permutation matrices and descending plane partitions  without special parts, which respects the quadruplet of statistics considered  by Behrend, Di Francesco and Zinn--Justin