A Beginner’s Guide to Edge and Cover Ideals

  • Adam Van TuylEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2083)


Monomial ideals, although intrinsically interesting, play an important role in studying the connections between commutative algebra and combinatorics. Broadly speaking, problems in combinatorics are encoded into monomial ideals, which then allow us to use techniques and methods in commutative algebra to solve the original question. Stanley’s proof of the Upper Bound Conjecture [180] for simplicial spheres is seen as one of the early highlights of exploiting this connection between two fields. To bridge these two areas of mathematics, Stanley used square-free monomial ideals.


Simplicial Complex Chromatic Number Commutative Algebra Betti Number Linear 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.



I would like to thank the organizers of MONICA, Anna M. Bigatti, Philippe Gimenez, and Eduardo Sáenz-de-Cabezón, for the invitation to participate in this conference. As well, I would like to thank all the participants for stimulating discussions and their feedback. I would also like to thank Ben Babcock, Ashwini Bhat, Jen Biermann, Chris Francisco, Tai Hà, Andrew Hoefel, and Ştefan Tohǎneanu for their feedback on preliminary drafts. The author was supported in part by an NSERC Discovery Grant.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesLakehead UniversityThunder BayCanada

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