Transport measurements of the activation gap at fractional filling factor 1/3 are compared to results of exact diagonalization, allowing identification of a small anti-skyrmion as the lowest excitation in the low-field regime. In agreement with theory, a crossover to spinless excitations at higher electron densities is observed. Two samples of different quality are investigated. A detailed description of the theoretical calculation of activation gaps is presented and features which should be taken into account are summarized: finite thickness, Landau level mixing, and comparison between different sizes of the model system and-whenever possible-also between different geometries (torus and sphere). Within the chosen model of disorder (entailing a single fit parameter) we obtain a good agreement between calculated energies and experimental results. © 2006 The American Physical Society.