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Generalization of Schensted insertion algorithm to the cases of hooks and semi-shuffles

Mikhail Kogan
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Abstract

Given an rc-graph $R$ of permutation $w$ and an rc-graph $Y$ of permutation $v$, we provide an insertion algorithm, which defines an rc-graph $R\leftarrow Y$ in the case when $v$ is a shuffle with the descent at $r$ and $w$ has no descents greater than $r$ or in the case when $v$ is a shuffle, whose shape is a hook. This algorithm gives a combinatorial rule for computing the generalized Littlewood-Richardson coefficients $c^{u}_{wv}$ in the two cases mentioned above.

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Mikhail Kogan. 2002-06-05. Generalization of Schensted insertion algorithm to the cases of hooks and semi-shuffles. https://arxiv.org/abs/math/0206045

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