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Berkesch, Christine; Brubaker, Benjamin; Musiker, Gregg; Pylyavskyy, Pavlo; Reiner, Victor (Ed.)Composing two representations of the general linear groups gives rise to Littlewood’s (outer) plethysm. On the level of characters, this poses the question of finding the Schur expansion of the plethysm of two Schur functions. A combinatorial interpretation for the Schur expansion coefficients of the plethysm of two Schur functions is, in general, still an open problem. We identify a proof technique of combinatorial representation theory, which we call the “s-perp trick”, and point out several examples in the literature where this idea is used. We use the s-perp trick to give algorithms for computing monomial and Schur expansions of symmetric functions. In several special cases, these algorithms are more efficient than those currently implemented in SageMath.more » « less
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We generalize the Robinson–Schensted–Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to an algorithm from parti- tion 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.more » « less
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