2026-09-19T17:16:49Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/646122022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Alexander Postnikov.
Desjardins, Craig J. (Craig Jeffrey)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2011-06-20T16:00:23Z
2011-06-20T16:00:23Z
2010
2010
http://hdl.handle.net/1721.1/64612
727165511
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 47-48).
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.
by Craig J. Desjardins.
Ph.D.
48 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Monomization of power Ideals and parking functions
Thesis
application/pdf
Publication
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