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

We present a bijection between permutation matrices and descending plane partitions without special parts, which respects the quadruple of statistics considered by Behrend, Di Francesco and Zinn–Justin. This bijection involves the inversion words of permutations and the “usual” representation of descending plane partitions as families of non–intersec-ting lattice paths.