N ov 2 00 3 BOTTOM SCHUR FUNCTIONS

We give a basis for the space spanned by the sumˆs λ of the lowest degree terms in the expansion of the Schur symmetric functions s λ in terms of the power sum symmetric functions p µ , where deg(p i) = 1. These lowest degree terms correspond to minimal border strip tableaux of λ. The dimension of the space spanned byˆs λ , where λ is a partition of n, is equal to the number of partitions of n into parts differing by at least 2. Applying the Rogers-Ramanujan identity, the generating function also counts the number of partitions of n into parts 5k + 1 and 5k − 1. We also show that a symmetric function closely related tô s λ has the same coefficients when expanded in terms of power sums or augmented monomial symmetric functions.