Bottom Schur Functions - Clifford, Peter; Stanley, Richard P. (The Electronic Journal of Combinatorics, 2004)
We give a basis for the space spanned by the sum s_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 by s_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 to s_λ has the same coefficients when expanded in terms of power sums or augmented monomial symmetric functions.