2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139457Rigged configurations are combinatorial objects originating from the Bethe Ansatz, that label highest weight crystal elements. In this paper a new unrestricted set of rigged configurations is introduced for types ADE by constructing a crystal structure on the set of rigged configurations. In type A an explicit characterization of unrestricted rigged configurations is provided which leads to a new fermionic formula for unrestricted Kostka polynomials or q-supernomial coefficients. The affine crystal structure for type A is obtained as well.20 pages, 1 figure, axodraw and youngtab style file necessaryQuantum AlgebraCombinatorics17B37; 81R50; 82B23; 05A19text