Monomization of power Ideals and parking functions

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2010

Author dc:creator

• Desjardins, Craig J. (Craig Jeffrey)

Advisor dc:contributor.advisor

• Alexander Postnikov.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/64612

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/64612