Computing Hilbert Functions using the Syzygy and LCM-lattice methods

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dc.contributor.advisor Agarwal, Anurag
dc.contributor.advisor Marengo, James
dc.contributor.author Barouti, Maria
dc.date.accessioned 2011-09-15T17:09:25Z
dc.date.available 2011-09-15T17:09:25Z
dc.date.issued 2011-08
dc.identifier.uri http://hdl.handle.net/1850/14145
dc.description.abstract The Hilbert function for any graded module over a field k is defined by the dimension of all of the summands M_b, where b indicates the graded component being considered. One standard approach to computing the Hilbert function is to come up with a free-resolution for the graded module M and another is via a Hilbert power series which serves as a generating function. Using combinatorics and homological algebra we develop three alternative ways to generate the values of a Hilbert function when the graded module is a quotient ring over a field. Two of these approaches (which we've called the lcm-Lattice method and the Syzygy method) are conceptually combinatorial and work for any polynomial quotient ring over a field. The third approach, which we call the Hilbert function table method, also uses syzygies but the approach is better described in terms of homological algebra. en_US
dc.language.iso en_US en_US
dc.subject None provided en_US
dc.subject.lcc QA273.6 .B37 2011
dc.subject.lcsh Characteristic functions en_US
dc.subject.lcsh Combinatorial analysis en_US
dc.subject.lcsh Algebra, Homological en_US
dc.title Computing Hilbert Functions using the Syzygy and LCM-lattice methods en_US
dc.type Thesis en_US
dc.description.college College of Science en_US
dc.description.department School of Mathematical Sciences en_US
dc.contributor.advisorChair Lopez, Manuel

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