Zero-bias anomalies in the conductance through quantum dots have recently b
een identified as Kondo resonances and explained in terms of the Anderson i
mpurity model. The effect requires a degeneracy and it has been proposed th
at this should occur for odd electron numbers on the dot. In this paper we
present data, obtained on a split-gate quantum dot with a small number of e
lectrons, which are in disagreement with this expectation. The mapping of t
he Anderson model on the quantum dot is discussed in terms of an interactin
g N electron system demonstrating why this expectation can fail.