A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants

DOI10.1016/j.aim.2011.04.013zbMath1258.13020OpenAlexW2157675040MaRDI QIDQ549220

James Haglund

Publication date: 7 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.aim.2011.04.013

zbMATH Keywords

Hilbert seriesMacdonald polynomialsdiagonal harmonicsdiagonal coinvariants

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Symmetric functions and generalizations (05E05) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Combinatorial aspects of commutative algebra (05E40)

Related Items (12)

A weighted sum over generalized Tesler matrices ⋮ Tail positive words and generalized coinvariant algebras ⋮ A polynomial expression for the character of diagonal harmonics ⋮ Constant term methods in the theory of Tesler matrices and Macdonald polynomial operators ⋮ Ehrhart positivity of Tesler polytopes and Berline-Vergne's valuation ⋮ Generalized \(q,t\)-Catalan numbers ⋮ The representation of the symmetric group on \(m\)-Tamari intervals ⋮ Kostant's partition function and magic multiplex juggling sequences ⋮ Refined knot invariants and Hilbert schemes ⋮ The polytope of Tesler matrices ⋮ Flow Polytopes and the Space of Diagonal Harmonics ⋮ Volumes and Ehrhart polynomials of flow polytopes

Cites Work

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• Hyperplane arrangements and diagonal harmonics
• Conjectures on the quotient ring by diagonal invariants
• Plethystic formulas for Macdonald \(q,t\)-Kostka coefficients
• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions
• A combinatorial formula for the character of the diagonal coinvariants
• A proof of the \(q,t\)-Catalan positivity conjecture
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• A conjectured combinatorial formula for the Hilbert series for diagonal harmonics

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