Combinatorial theory of Macdonald polynomials I: Proof of Haglund's formula - Haglund, J. (National Academy of Sciences, 2005)
Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H̃(μ). We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H̃(μ). As corollaries, we obtain the cocharge formula of Lascoux and Schützenberger for Hall–Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials J(μ), a formula for H̃(μ) in terms of Lascoux–Leclerc–Thibon polynomials, and combinatorial expressions for the Kostka–Macdonald coefficients K̃(λ,μ) when μ is a two-column shape.