On inequalities for normalized Schur functions
Abstract
We prove a conjecture of Cuttler et al.~[2011] [A. Cuttler, C. Greene, and M. Skandera; Inequalities for symmetric means. European J. Combinatorics, 32(2011), 745--761] on the monotonicity of normalized Schur functions under the usual (dominance) partial-order on partitions. We believe that our proof technique may be helpful in obtaining similar inequalities for other symmetric functions.
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