Scott Greenleaf - Boston University
Polynomials and the Action of S3
The polynomials are an important class of functions in mathematics. During this talk, we will restrict our attention to polynomials in three variables. The symmetric group S3 is the set of permutations of three objects. For instance, one may regard S3 as the group of symmetries of an equilateral triangle. We consider what interaction these two sets, the polynomials and S3, have with each other. We look at polynomials which behave in a particularly nice way when their variables are permuted, and this leads us to a decomposition of polynomials with respect to the action of S3.
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