Haglund's conjecture on 3-column Macdonald polynomials

DOI10.1007/s00209-015-1612-7zbMath1344.05147arXiv1411.3646OpenAlexW2116960419WikidataQ122901590 ScholiaQ122901590MaRDI QIDQ284823

Jonah Blasiak

Publication date: 18 May 2016

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.3646

zbMATH Keywords

\(q\)-Littlewood-Richardson coefficientsinversion numberLLT polynomialsflagged Schur functionsnoncommutative Schur functions

Mathematics Subject Classification ID

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

Related Items (12)

Abacus proofs of Schur expansions of Macdonald polynomials ⋮ Toward the Schur expansion of Macdonald polynomials ⋮ What makes a \(\mathbf D_0\) graph Schur positive? ⋮ Variants of the RSK algorithm adapted to combinatorial Macdonald polynomials ⋮ Colored fermionic vertex models and symmetric functions ⋮ Cyclic sieving, skew Macdonald polynomials and Schur positivity ⋮ Rules of three for commutation relations ⋮ Modified Macdonald polynomials and integrability ⋮ Noncommutative Schur functions, switchboards, and Schur positivity ⋮ Kronecker coefficients and noncommutative super Schur functions ⋮ Linear relations on LLT polynomials and their \(k\)-Schur positivity for \(k=2\) ⋮ LLT cumulants and graph coloring

Cites Work

• Unnamed Item
• Unnamed Item
• Noncommutative Schur functions, switchboards, and Schur positivity
• Shifted dual equivalence and Schur \(P\)-positivity
• Flagged Schur functions, Schubert polynomials, and symmetrizing operators
• Some combinatorial properties of Schubert polynomials
• Some bijective correspondences involving domino tableaux
• Noncommutative Schur functions and their applications
• A combinatorial formula for the character of the diagonal coinvariants
• Positivity for special cases of \((q,t)\)-Kostka coefficients and standard tableaux statistics
• Splitting the square of a Schur function into its symmetric and antisymmetric parts
• Dual equivalence graphs revisited and the explicit Schur expansion of a family of LLT polynomials
• Ribbon Schur operators
• A generalized major index statistic
• Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties
• A combinatorial formula for Macdonald polynomials
• Statistics for Special q, t-Kostka Polynomials
• A combinatorial model for the Macdonald polynomials

This page was built for publication: Haglund's conjecture on 3-column Macdonald polynomials