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Unformatted text preview: 3 3 .2;1/ C 3 3 . Of course, such computations can be automated. A program in Mathematica for expanding symmetric polynomials in elementary symmetric functions is available on my World Wide Web site. 1 Exercises 9.6 9.6.1. (a) Show that the set K d x 1 ;:::;x n of polynomials that are homogeneous of total degree d or identically zero is a nitedimensional vector subspace of the Kvector space Kx 1 ;:::;x n . (b) Find the dimension of K d x 1 ;:::;x n . (c) Show that Kx 1 ;:::;x n is the direct sum of K d x 1 ;:::;x n , where d ranges over the nonnegative integers. 9.6.2. Prove Lemma 9.6.1 . 9.6.3. (a) For each d , K d x 1 ;:::;x n is invariant under the action of S n . 1 www.math.uiowa.edu/~ goodman...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra

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