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Séminaire Lotharingien de Combinatoire, 84B.48 (2020), 12 pp.

# Laura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling and Mike Zabrocki

# An Insertion Algorithm for Diagram Algebras

**Abstract.**
We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets.
This generalization leads to an algorithm from partition diagrams to pairs of a standard tableau and a standard
multiset tableau of the same shape, which has the remarkable property that it is well-behaved with respect to
restricting a representation to a subalgebra. This insertion algorithm matches recent representation-theoretic
results of Halverson and Jacobson.

Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.

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