A proof of the \(q,t\)-square conjecture

DOI10.1016/j.jcta.2006.01.002zbMath1110.05098OpenAlexW2085858850WikidataQ123154639 ScholiaQ123154639MaRDI QIDQ855837

Nicholas A. Loehr, Mahir Bilen Can

Publication date: 7 December 2006

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2006.01.002

zbMATH Keywords

symmetric functionMacdonald polynomialsplethysm\((q,t)\)-Catalan numbersBergeron-Garsia nabla operatorsquare lattice paths

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Symmetric functions and generalizations (05E05) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

Related Items (7)

A proof of the square paths conjecture ⋮ A valley version of the delta square conjecture ⋮ Decorated Dyck Paths, Polyominoes, and the Delta Conjecture ⋮ Limits of modified higher \(q,t\)-Catalan numbers ⋮ Theta operators, refined delta conjectures, and coinvariants ⋮ Sweep maps: a continuous family of sorting algorithms ⋮ Delta conjectures

Cites Work

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• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• \(t,q\)-Catalan numbers and the Hilbert scheme.
• 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
• Lagrange inversion and Schur functions
• A positivity result in the theory of Macdonald polynomials
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• Square $\boldsymbol {q,t}$-lattice paths and $\boldsymbol {\nabla (p_n)}$

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