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Bottom Schur functions

Peter Clifford·Richard P. Stanley
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Abstract

We give a basis for the space V spanned by the lowest degree part \hat{s}_λof the expansion of the Schur symmetric functions s_λin terms of power sums, where we define the degree of the power sum p_i to be 1. In particular, the dimension of the subspace V_n spanned by those \hat{s}_λfor which λis a partition of n is equal to the number of partitions of n whose parts differ by at least 2. We also show that a symmetric function closely related to \hat{s}_λhas the same coefficients when expanded in terms of power sums or augmented monomial symmetric functions. Proofs are based on the theory of minimal border strip decompositions of Young diagrams.

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Peter Clifford, Richard P. Stanley. 2004-09-20. Bottom Schur functions. https://arxiv.org/abs/math/0311382

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