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Fomin (1994) introduced a notion of duality between two graded graphs on thesame set of vertices. He also introduced a generalization to dual graded graphsof the classical Robinson-Schensted-Knuth algorithm. We show how Fomin'sapproach applies to the binary search tree insertion algorithm also known assylvester insertion, and to the hypoplactic insertion algorithm.

Binary Search Tree insertion, the Hypoplactic insertion, and Dual Graded Graphs