A combinatorial formula for Macdonald polynomials

From MaRDI portal

Publication:4679404

Jump to:navigation, search

DOI10.1090/S0894-0347-05-00485-6zbMath1061.05101OpenAlexW2963339095MaRDI QIDQ4679404

Nicholas A. Loehr, James Haglund, Mark D. Haiman

Publication date: 30 May 2005

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0894-0347-05-00485-6

zbMATH Keywords

Jack polynomials Hall-Littlewood polynomials charge formula Kostka-Macdonald coefficients

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Combinatorial aspects of representation theory (05E10)

Related Items

Quasisymmetric and Schur expansions of cycle index polynomials, A combinatorial expansion of vertical-strip LLT polynomials in the basis of elementary symmetric functions, Parabolic Kazhdan-Lusztig polynomials of type \(-1\) for quasi-minuscule quotients, Parabolic Kazhdan-Lusztig polynomials for quasi-minuscule quotients, Positivity among \(P\)-partition generating functions, Haglund's conjecture on 3-column Macdonald polynomials, Macdonald cumulants, \(G\)-inversion polynomials and \(G\)-parking functions, A combinatorial approach to the \(q,t\)-symmetry relation in Macdonald polynomials, A \(k\)-tableau characterization of \(k\)-Schur functions, Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials, A combinatorial formula for Macdonald cumulants, Crystal graphs, key tabloids, and nonsymmetric Macdonald polynomials, On the Schur expansion of Jack polynomials, Toward the Schur expansion of Macdonald polynomials, Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials, A product formula for certain Littlewood-Richardson coefficients for Jack and Macdonald polynomials, What makes a \(\mathbf D_0\) graph Schur positive?, Variants of the RSK algorithm adapted to combinatorial Macdonald polynomials, Plethysms of chromatic and Tutte symmetric functions, A weighted sum over generalized Tesler matrices, Quasisymmetric and noncommutative skew Pieri rules, Combinatorics of the two-species ASEP and Koornwinder moments, A major-index preserving map on fillings, A combinatorial formula for Macdonald polynomials, A bijective proof of a factorization formula for specialized Macdonald polynomials, Modules of the 0-Hecke algebra and quasisymmetric Schur functions, Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions, Quasisymmetric Schur functions, 0-Hecke algebra actions on coinvariants and flags, A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials, A refinement of the Murnaghan-Nakayama rule by descents for border strip tableaux, Multispecies TAZRP and modified Macdonald polynomials, Orbit harmonics and cyclic sieving: a survey, Fundamental expansion of quasisymmetric Macdonald polynomials, Applications of a Laplace-Beltrami operator for Jack polynomials, Poincaré polynomials of character varieties, Macdonald polynomials and affine Springer fibers, Macdonald polynomials and chromatic quasisymmetric functions, A computational and combinatorial exposé of plethystic calculus, Hall-Littlewood polynomials, alcove walks, and fillings of Young diagrams, Parabolic Kazhdan-Lusztig \(R\)-polynomials for tight quotients of the symmetric groups., On the combinatorics of LLT polynomials in \(Sp_{2n}\), Ordered set partitions, Tanisaki ideals, and rank varieties, Skew quasisymmetric Schur functions and noncommutative Schur functions, Cyclic sieving, skew Macdonald polynomials and Schur positivity, An extension of MacMahon's equidistribution theorem to ordered multiset partitions, A new recursion in the theory of Macdonald polynomials, Modified Macdonald polynomials and the multispecies zero-range process. I, The Delta Conjecture, Generalization of the Macdonald formula for Hall-Littlewood polynomials, Haglund's conjecture for multi-\(t\) Macdonald polynomials, A \(q\)-multinomial expansion of LLT coefficients and plethysm multiplicities, Motivic Donaldson-Thomas invariants of parabolic Higgs bundles and parabolic connections on a curve, A generalization of Newton's identity and Macdonald functions, From Macdonald polynomials to a charge statistic beyond type \(A\), Unnamed Item, A proof of the shuffle conjecture, Modified Macdonald polynomials and integrability, An iterative formula for the Kostka-Foulkes polynomials, Parabolic Kazhdan-Lusztig \(R\)-polynomials for Hermitian symmetric pairs., Noncommutative Schur functions, switchboards, and Schur positivity, Dual equivalence graphs revisited and the explicit Schur expansion of a family of LLT polynomials, Kazhdan-Lusztig polynomials of Boolean elements, On the Schur expansion of Hall-Littlewood and related polynomials via Yamanouchi words, On combinatorial formulas for MacDonald polynomials, A probabilistic interpretation of the Macdonald polynomials, Isomorphisms of Hecke modules and parabolic Kazhdan-Lusztig polynomials., Hopf algebra structure of symmetric and quasisymmetric functions in superspace, Rigidity for the Hopf algebra of quasisymmetric functions, An analogue of the Robinson-Schensted-Knuth correspondence and non-symmetric Cauchy kernels for truncated staircases, Narayana polynomials and Hall-Littlewood symmetric functions, Noncommutative unicellular LLT polynomials, Multi-Macdonald polynomials, Backward jeu de taquin slides for composition tableaux and a noncommutative Pieri rule, From quasisymmetric expansions to Schur expansions via a modified inverse Kostka matrix, LLT polynomials, elementary symmetric functions and melting lollipops, Kazhdan-Lusztig polynomials, tight quotients and Dyck superpartitions., Asymptotic normality of the major index on standard tableaux, Nonsymmetric Macdonald polynomials and a refinement of Kostka–Foulkes polynomials, Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials, Demazure crystals for specialized nonsymmetric Macdonald polynomials, Linear relations on LLT polynomials and their \(k\)-Schur positivity for \(k=2\), LLT polynomials, chromatic quasisymmetric functions and graphs with cycles, A Murnaghan-Nakayama rule for noncommutative Schur functions, Parabolic Kazhdan-Lusztig polynomials, plethysm and generalized Hall-Littlewood functions for classical types, A Schur-like basis of \(\mathsf{NSym}\) defined by a Pieri rule, \(e\)-positivity of vertical strip LLT polynomials, An explicit construction of type A Demazure atoms, \(P\)-partitions and \(p\)-positivity, Delta conjectures, From multiline queues to Macdonald polynomials via the exclusion process, Macdonald polynomials and cyclic sieving, Difference equations and Pieri formulas for \(G_2\) type Macdonald polynomials and integrability, Colorful combinatorics and Macdonald polynomials, Tableau posets and the fake degrees of coinvariant algebras, The valley version of the extended delta conjecture, Newton polytopes in algebraic combinatorics, Cylindric rhombic tableaux and the two-species ASEP on a ring, LLT cumulants and graph coloring, A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers, A summation formula for Macdonald polynomials, Abacus proofs of Schur expansions of Macdonald polynomials, Set superpartitions and superspace duality modules, Colored fermionic vertex models and symmetric functions, A proof of the \(\frac{n!}{2}\) conjecture for hook shapes, Skew RSK dynamics: Greene invariants, affine crystals and applications toq-Whittaker polynomials, Expanding the quasisymmetric Macdonald polynomials in the fundamental basis, Horizontal-strip LLT polynomials, Haglund's positivity conjecture for multiplicity one pairs, A \(\mathrm{GL}(\mathbb{F}_q)\)-compatible Hopf algebra of unitriangular class functions, Hopf dreams and diagonal harmonics, Delta and Theta Operator Expansions, Springer fibers and the Delta Conjecture at \(t = 0\), A horizontal-strip LLT polynomial is determined by its weighted graph, Matrix product and sum rule for Macdonald polynomials, Torus link homology and the nabla operator, Parabolic Kazhdan-Lusztig \(R\)-polynomials for quasi-minuscule quotients, Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials, Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials, Unnamed Item, Harmonic bases for generalized coinvariant algebras, Harmonic bases for generalized coinvariant algebras, A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials, A refinement of the Murnaghan-Nakayama rule by descents for border strip tableaux, From multiline queues to Macdonald polynomials via the exclusion process, Ordered set partitions, Garsia-Procesi modules, and rank varieties, A Shuffle Theorem for Paths Under Any Line

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:4679404&oldid=18898162"