Download or read book Computing Hilbert Functions Using the Syzygy and LCM-lattice Methods written by Maria Barouti and published by . This book was released on 2011 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."--Abstract.