Macdonald cumulants, \(G\)-inversion polynomials and \(G\)-parking functions

DOI10.1016/j.ejc.2018.08.011zbMath1400.05266arXiv1707.02656OpenAlexW2735654422MaRDI QIDQ1623876

Maciej Dołęga

Publication date: 15 November 2018

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

Full work available at URL: https://arxiv.org/abs/1707.02656

zbMATH Keywords

Jack polynomialsHall-Littlewood polynomialscharge formulaKostka-Macdonald coefficients

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of representation theory (05E10)

Related Items (2)

A positive combinatorial formula for symplectic Kostka-Foulkes polynomials. I: Rows ⋮ LLT cumulants and graph coloring

Cites Work

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• On the matchings-Jack conjecture for Jack connection coefficients indexed by two single part partitions
• Gaussian fluctuations of Young diagrams and structure constants of Jack characters
• Asymptotic behavior of some statistics in Ewens random permutations
• A rooted map invariant, non-orientability and Jack symmetric functions
• Green polynomials and singularities of unipotent classes
• Chip firing and the Tutte polynomial
• A combinatorial formula for the character of the diagonal coinvariants
• Fluctuations of particle systems determined by Schur generating functions
• Enumerative applications of a decomposition for graphs and digraphs
• The Tutte polynomial of a graph, depth-first search, and simplicial complex partitions
• Hecke algebras at roots of unity and crystal bases of quantum affine algebras
• Strong factorization property of Macdonald polynomials and higher-order Macdonald's positivity conjecture
• A weighted sum over generalized Tesler matrices
• Top degree part in \(b\)-conjecture for unicellular bipartite maps
• Asymptotics of \(q\)-Plancherel measures.
• Combinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics
• Macdonald processes
• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• Cumulants of the q-semicircular Law, Tutte Polynomials, and Heaps
• The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture
• Compositional (km,kn)-Shuffle Conjectures
• The Delta Conjecture
• A proof of the shuffle conjecture
• A combinatorial formula for Macdonald polynomials
• Trees, parking functions, syzygies, and deformations of monomial ideals
• Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions
• Chromatic quasisymmetric functions and Hessenberg varieties
• A graded representation model for Macdonald's polynomials.
• Schur positivity and Schur log-concavity
• A Contribution to the Theory of Chromatic Polynomials

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