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

2002/06/05 by Mikhail Kogan, М. Н. Коган, Kogan, Mikhail
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Blind Source Separation Techniques #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0206045

22 pages

arxiv created 2002/06/05 · openalex publication_date 2002/06/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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← 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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