# Computing Hilbert Functions using the Syzygy and LCM-lattice methods

 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. en_US 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. dc.language.iso en_US en_US dc.relation RIT Scholars content from RIT Digital Media Library has moved from http://ritdml.rit.edu/handle/1850/14145 to RIT Scholar Works http://scholarworks.rit.edu/theses/4802, please update your feeds & links! 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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