Monomization of power Ideals and parking functions
Name
727165511-MIT.pdf
Description
Full printable version
Size
1.99 MB
Format
Adobe PDF
Checksum (MD5)
6fed81e05bc0e96bc2c79ef9005d01aa
Author(s)
Desjardins, Craig J. (Craig Jeffrey)
Advisor(s)
Alexander Postnikov.
Date Issued
2010
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 47-48).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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