Monomial Ideals and Planar Graphs

  • Ezra Miller
  • Bernd Sturmfels
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1719)


Gröbner basis theory reduces questions about systems of polynomial equations to the combinatorial study of monomial ideals, or staircases. This article gives an elementary introduction to current research in this area. After reviewing the bivariate case, a new correspondence is established between planar graphs and minimal resolutions of monomial ideals in three variables. A brief guide is given to the literature on complexity issues and monomial ideals in four or more variables.


Planar Graph Irreducible Component Hilbert Series Monomial Ideal Free Resolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Ezra Miller
    • 1
  • Bernd Sturmfels
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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