Bottom Schur functions
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
16 pages, 13 figures To appear in the Electronic Journal of Combinatorics
16 pages, 13 figures To appear in the Electronic Journal of Combinatorics