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تسجيل مستخدم جديدBottom Schur functions
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We give a basis for the space V spanned by the lowest degree part hat{s}_lambda of the expansion of the Schur symmetric functions s_lambda in 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}_lambda for which lambda is 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}_lambda has 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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