Planar decompositions of tableaux and Schur function determinants

DOI10.1016/0195-6698(95)90002-0zbMath0832.05097OpenAlexW1992114298MaRDI QIDQ1898051

Angèle M. Hamel, Ian P. Goulden

Publication date: 8 February 1996

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0195-6698(95)90002-0

zbMATH Keywords

shapeskew Schur functionsYoung tableauxdeterminantsymmetric functionsSchur functiontableaulattice pathdeterminantal identityGessel-Viennot lattice pathoutside decompositionplanar decompositionsSchur function determinants

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10)

Related Items (27)

The skew Schubert polynomials ⋮ Generalized Sylvester formulas and skew Giambelli identities ⋮ On Schur multiple zeta functions: a combinatoric generalization of multiple zeta functions ⋮ Towards a combinatorial classification of skew Schur functions ⋮ The Smith normal form of a specialized Giambelli-type matrix ⋮ Outside nested decompositions of skew diagrams and Schur function determinants ⋮ Generalized Jacobi-Trudi determinants and evaluations of Schur multiple zeta values ⋮ A planar network proof for Hankel total positivity of type \(B\) Narayana polynomials ⋮ Stanley's zrank conjecture on skew partitions ⋮ A generalization of the dual immaculate quasisymmetric functions in partially commutative variables ⋮ Hook Formulas for Skew Shapes II. Combinatorial Proofs and Enumerative Applications ⋮ Equivariant resolutions over Veronese rings ⋮ Determinantal and Pfaffian identities for ninthvariation skew Schur functions and \(Q\)-functions ⋮ Coincidences among skew Schur functions ⋮ Asymptotics of the number of standard Young tableaux of skew shape ⋮ The expansion of immaculate functions in the ribbon basis ⋮ Symmetric functions, tableaux decompositions and the fermion-boson correspondence ⋮ A generalization of the Littlewood-Richardson rule ⋮ The flagged double Schur function ⋮ Factorial supersymmetric skew Schur functions and ninth variation determinantal identities ⋮ On the Okounkov-Olshanski formula for standard tableaux of skew shapes ⋮ Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes ⋮ Division and the Giambelli identity ⋮ Generalized Schur Function Determinants Using the Bazin Identity ⋮ The zrank conjecture and restricted Cauchy matrices ⋮ Combinatorial and algebraic enumeration: a survey of the work of Ian P. Goulden and David M. Jackson ⋮ Determinantal formulas for dual Grothendieck polynomials

Cites Work

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• Nonintersecting paths, pfaffians, and plane partitions
• Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
• Ribbon Schur functions
• Pfaffians and determinants for Schur \(Q\)-functions
• Lattice path proof of the ribbon determinant formula for Schur functions

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