On the error bound in the normal approximation for Jack measures

In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in normal approximation for Jack deformations of character ratio, by using Stein’s method zero-bias couplings. Our bound comes very close to that conjectured Fulman (J. Combin. Theory Ser. A 108 (2004) 275–296). As a by-product proof bound, Rosenthal-type inequality