Lecture Notes in Mathematics

Monomial Ideals, Computations and Applications

Editors: Bigatti, Anna Maria, Gimenez, Philippe, Sáenz-de-Cabezón, Eduardo (Eds.)

  • Chapters cover leading-edge aspects of the theory of monomial ideals written by top researchers in their fields
  • Includes computer tutorials that highlight the computational aspects of the area
  • Carefully written introductions to topics of current research interest
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About this book

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez 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, Gröbner 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 (6 chapters)

  • A Survey on Stanley Depth

    Herzog, Jürgen

    Pages 3-45

  • Stanley Decompositions Using CoCoA

    Bigatti, Anna Maria (et al.)

    Pages 47-59

  • A Beginner’s Guide to Edge and Cover Ideals

    Tuyl, Adam

    Pages 63-94

  • Edge Ideals Using Macaulay2

    Tuyl, Adam

    Pages 95-105

  • Local Cohomology Modules Supported on Monomial Ideals

    Montaner, Josep Àlvarez

    Pages 109-178

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-38742-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-642-38741-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Monomial Ideals, Computations and Applications
Editors
  • Anna Maria Bigatti
  • Philippe Gimenez
  • Eduardo Sáenz-de-Cabezón
Series Title
Lecture Notes in Mathematics
Series Volume
2083
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-38742-5
DOI
10.1007/978-3-642-38742-5
Softcover ISBN
978-3-642-38741-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XI, 194
Number of Illustrations and Tables
42 b/w illustrations
Topics