Monomization of power Ideals and parking functions
Author(s)Desjardins, Craig J. (Craig Jeffrey)
Massachusetts Institute of Technology. Dept. of Mathematics.
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A zonotopal algebra is the quotient of a polynomial ring by an ideal generated by powers of linear forms which are derived from a zonotope, or dually it's hyperplane arrangement. In the case that the hyperplane arrangement is of Type A, we can rephrase the definition in terms of graphs. Using the symmetry of these ideals, we can find monomial ideals which preserve much of the structure of the zonotopal algebras while being computationally very efficient, in particular far faster than Gröbner basis techniques. We extend this monomization theory from the known case of the central zonotopal algebra to the other two main cases of the external and internal zonotopal algebras.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 47-48).
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology