Generalizations of the Coinvariant Algebra
- Author(s): Meyer, Kyle
- Advisor(s): Rhoades, Brendon
- et al.
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.