KIAS

ROOM 1409

*J*

_{λ}[

*X*;

*q*,

*q*

^{k}]/(1-

*q*)

^{n},

*s*

_{μ}(

*X*)⟩∈ℕ[

*q*], we have found explicit combinatorial formulas for the Schur coefficients in one row case, two column case and certain hook shape cases. Egge-Loehr-Warrington constructed a combinatorial way of getting Schur expansion of symmetric functions when the expansion of the function in terms of Gessel’s fundamental quasi symmetric functions is given. We apply this method to the combinatorial formula for the integral form Macdonlad polynomials of Haglund-Haiman-Loehr in quasi symmetric functions to get the Schur coefficients and prove the Haglund’s conjecture in more general cases.