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Monomial Ideals, Computations and Applications

  • Anna M. Bigatti
  • Philippe Gimenez
  • Eduardo Sáenz-de-Cabezón

Part of the Lecture Notes in Mathematics book series (LNM, volume 2083)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Stanley Decompositions

    1. Front Matter
      Pages 1-1
    2. Jürgen Herzog
      Pages 3-45
    3. Anna Maria Bigatti, Emanuela De Negri
      Pages 47-59
  3. Edge Ideals

    1. Front Matter
      Pages 61-61
    2. Adam Van Tuyl
      Pages 95-105
  4. Local Cohomology

    1. Front Matter
      Pages 107-107
    2. Josep Àlvarez Montaner
      Pages 109-178
    3. Josep Àlvarez Montaner, Oscar Fernández-Ramos
      Pages 179-185
  5. Back Matter
    Pages 187-196

About this book

Introduction

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.

Keywords

13-02,13C15,13D45,13F55 Computational aspects Edge Ideals Local cohomology Monomial Ideals Stanley depth

Editors and affiliations

  • Anna M. Bigatti
    • 1
  • Philippe Gimenez
    • 2
  • Eduardo Sáenz-de-Cabezón
    • 3
  1. 1.Universitá degli Studi di Genova Dipartimento di MatematicaGenovaItaly
  2. 2.Geometría y TopologíaUniversity of Valladolid, Dpto. de Álgebra, Análisis MatemáticoValladolidSpain
  3. 3.University of La Rioja Matemáticas y ComputaciónLogroñoSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-38742-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-38741-8
  • Online ISBN 978-3-642-38742-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site