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In this paper we first generalize to the case of partial flags a resultproved both by Spaltenstein and by Steinberg that relates the relative positionof two complete flags and the irreducible components of the flag variety inwhich they lie, using the Robinson-Schensted-Knuth correspondence. Then we usethis result to generalize the mirabolic Robinson-Schensted-Knuth correspondencedefined by Travkin, to the case of two partial flags and a line.

Classic and mirabolic Robinson-Schensted-Knuth correspondence for partial flags