A combinatorial formula for Macdonald cumulants

zbMath1411.05280MaRDI QIDQ2632680

Maciej Dołęga

Publication date: 15 May 2019

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: http://www.mat.univie.ac.at/~slc/wpapers/FPSAC2018//41-Dolega.html

zbMATH Keywords

cumulantsMacdonald polynomialsTutte polynomialsSchur polynomials\(G\)-parking functions\(q,t\)-Kostka numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10)

Cites Work

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• Chip firing and the Tutte polynomial
• Strong factorization property of Macdonald polynomials and higher-order Macdonald's positivity conjecture
• Top degree part in \(b\)-conjecture for unicellular bipartite maps
• Asymptotics of \(q\)-Plancherel measures.
• Macdonald processes
• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• A combinatorial formula for Macdonald polynomials
• Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions
• Cumulants of Jack symmetric functions and the $b$-conjecture

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