New fermionic formula for unrestricted Kostka polynomials

A new fermionic formula for the unrestricted Kostka polynomials of type A n − 1 ( 1 ) is presented. This formula is different from the one given by Hatayama et al. and is valid for all crystal paths based on Kirillov–Reshetikhin modules, not just for the symmetric and antisymmetric case. The fermionic formula can be interpreted in terms of a new set of unrestricted rigged configurations. For the proof a statistics preserving bijection from this new set of unrestricted rigged configurations to the set of unrestricted crystal paths is given which generalizes a bijection of Kirillov and Reshetikhin.