Bottom Schur functions

2003/11/21 by Peter Clifford, Richard P. Stanley, Clifford, Peter +1
Mathematics · #05E05 #05E10 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E05 #msc:05E10

paper · pdf · doi:10.48550/arxiv.math/0311382

16 pages, 13 figures To appear in the Electronic Journal of Combinatorics

openalex publication_date 2003/11/21 · arxiv created 2004/09/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a basis for the space V spanned by the lowest degree part 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 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 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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