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Generalizations of the Coinvariant Algebra


The classical coinvariant algebra is the quotient of the polynomial ring in n variables by the ideal generated by polynomials that are invariant under the action of variable permutation. The classical coinvariant algebra is a fundamental object of study in the theory of algebraic combinatorics and a variety of generalizations of it have been defined. In this dissertation we will explore a variety of generalizations and refinements of the coinvariant algebra.

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