A combinatorial approach to the \(q,t\)-symmetry relation in Macdonald polynomials

zbMath1337.05109arXiv1503.02109MaRDI QIDQ289979

Maria Monks Gillespie

Publication date: 1 June 2016

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.02109

zbMATH Keywords

Young tableauxMacdonald polynomialsMahonian statisticsHall-Littlewood polynomialscochargeGarsia-Procesi modules

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

Related Items (4)

Higher Specht bases for generalizations of the coinvariant ring ⋮ A bijective proof of Macdonald's reduced word formula ⋮ Ordered set partitions, Garsia-Procesi modules, and rank varieties ⋮ A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers

Cites Work

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• A proof of the \(n!\) conjecture for generalized hooks
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• A kicking basis for the two-column Garsia-Haiman modules
• A Combinatorial Property of q-Eulerian Numbers
• Major Index and Inversion Number of Permutations
• Some Particular Entries of the Two-Parameter Kostka Matrix
• A combinatorial formula for Macdonald polynomials
• Statistics for Special q, t-Kostka Polynomials
• An Eulerian partner for inversions

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