Schensted algorithms for dual graded graphs
Journal of Algebraic Combinatorics, Tome 4 (1995) no. 1, pp. 5-45.

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Summary: This paper is a sequel to [3]. We keep the notation and terminology and extend the numbering of sections, propositions, and formulae of [3]. The main result of this paper is a generalization of the Robinson-Schensted correspondence to the class of dual graded graphs introduced in [3], This class extends the class of $Y$-graphs, or differential posets [22], for which a generalized Schensted correspondence was constructed earlier in [2].
Mots-clés : discrete algorithm, enumerative combinatorics, poset, Young diagram 
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Fomin, Sergey. Schensted algorithms for dual graded graphs. Journal of Algebraic Combinatorics, Tome 4 (1995) no. 1, pp. 5-45. https://geodesic-test.mathdoc.fr/item/JAC_1995__4_1_a2/