A polynomial expression for the character of diagonal harmonics

DOI10.1007/s00026-015-0284-7zbMath1326.05007OpenAlexW2119306125MaRDI QIDQ891953

Adriano M. Garsia, James Haglund

Publication date: 18 November 2015

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

Full work available at URL: https://doi.org/10.1007/s00026-015-0284-7

zbMATH Keywords

Macdonald polynomialscharacter of diagonal harmonicsTesler matrices

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Symmetric functions and generalizations (05E05) Symmetric groups (20B30)

Related Items

A weighted sum over generalized Tesler matrices ⋮ On the poset and asymptotics of Tesler matrices ⋮ Flow Polytopes and the Space of Diagonal Harmonics

Cites Work

• Unnamed Item
• Rational parking functions and Catalan numbers
• Refined knot invariants and Hilbert schemes
• A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants
• 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
• Compactified Jacobians and \(q,t\)-Catalan numbers. I.
• A combinatorial formula for the character of the diagonal coinvariants
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• Compactified Jacobians and \(q,t\)-Catalan numbers. II
• Combinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics
• Affine Springer fibers of type \(A\) and combinatorics of diagonal coinvariants