Monomial ideals, computations and applications
Author(s)
Bibliographic Information
Monomial ideals, computations and applications
（Lecture notes in mathematics, 2083）
Springer, c2013
Available at 44 libraries
Note
Includes bibliographical references (p. 187-194)
Description and Table of Contents
Description
This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jurgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Alvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Groebner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.
Table of Contents
A survey on Stanley depth.- Stanley decompositions using CoCoA.- A beginner's guide to edge and cover ideals.- Edge ideals using Macaulay2.- Local cohomology modules supported on monomial ideals.- Local Cohomology using Macaulay2.
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