A simple proof of the Littlewood-Richardson rule and applications.

DOI10.1016/S0012-365X(98)00145-9zbMath1061.05507MaRDI QIDQ1584473

Mark Shimozono, Jeffery B. Remmel

Publication date: 2 November 2000

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

involutionplethysmSchur function expansion

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05)

Related Items (15)

A Littlewood-Richardson rule for dual stable Grothendieck polynomials ⋮ The combinatorics of Jeff Remmel ⋮ A combinatorial proof of the reduction formula for Littlewood-Richardson coefficients ⋮ The combinatorics of transition matrices between the bases of the symmetric functions and the \(B_ n\) analogues ⋮ Noncommutative LR coefficients and crystal reflection operators ⋮ A generalized SXP rule proved by bijections and involutions ⋮ Why should the Littlewood–Richardson Rule be true? ⋮ Equivariant Littlewood-Richardson skew tableaux ⋮ Skew Schubert functions and the Pieri formula for flag manifolds ⋮ Vanishing ideals of lattice diagram determinants ⋮ Schur partial derivative operators ⋮ Structure constants for \(K\)-theory of Grassmannians, revisited ⋮ Bases for coordinate rings of conjugacy classes of nilpotent matrices ⋮ Littlewood-Richardson rules for Grassmannians ⋮ ALGORITHM FOR MULTIPLYING SCHUBERT CLASSES

Cites Work

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• Binomial determinants, paths, and hook length formulae
• Some connections between the Littlewood-Richardson rule and the construction of Schensted
• A Littlewood-Richardson miscellany
• Crystal graphs and \(q\)-analogues of weight multiplicities for the root system \(A_ n\)
• Multiplying Schur functions
• A combinatorial interpretation of the inverse kostka matrix
• Group characters and algebra
• A combinatorial rule for the schur function expansion of the PlethysmS(1^a,b)[P_k]
• A cyclage poset structure for Littlewood-Richardson tableaux
• Littlewood-Richardson without algorithmically defined bijections

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