RC-graphs and a generalized Littlewood-Richardson rule (Q2746853)
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scientific article; zbMATH DE number 1656645
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | RC-graphs and a generalized Littlewood-Richardson rule |
scientific article; zbMATH DE number 1656645 |
Statements
2 October 2002
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Schubert polynomials
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Schur functions
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Littlewood-Richardson rule
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Monk's rule
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Pieri's rule
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RC-graphs
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RC-graphs and a generalized Littlewood-Richardson rule (English)
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How to multiply two Schubert polynomials is a notorious open problem in Schubert calculus. The author addresses the special case where a Schubert polynomial is multiplied by a Schur polynomial. His result is a (not very efficient but still beautiful) description of the expansion coefficients in this product as the number of pairs of an RC-graph as introduced by \textit{S. Fomin} and \textit{A. N. Kirillov} [Discrete Math. 153, 123-143 (1996; Zbl 0852.05078)] and a Young tableau, which have to be related in a certain way. The proof of this result is entirely based on the insertion algorithm for RC-graphs due to \textit{N. Bergeron} and \textit{S. Billey} [Exp. Math. 2, 257-269 (1993; Zbl 0803.05054)].
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