Warning: I do not know nothing about combinatorial problems, so what I say now might be completely wrong. However: Rota in his talk at the Birkhoff memorial conference (The many lives of lattice theory, easily available online) has, in the section about semiprimary lattices, something which seemes strongly related.
Edit: citing from the article: each of the two chains is associated with a standard Young tableau, hence we obtain the statement and proof of the Schensted algorithm, which precisely associates a pair of standard Young tableaux to every permutation.
