manuscripta mathematica

, Volume 109, Issue 2, pp 159–174 | Cite as

The facet ideal of a simplicial complex

  • Sara Faridi


 To a simplicial complex, we associate a square-free monomial ideal in the polynomial ring generated by its vertex set over a field. We study algebraic properties of this ideal via combinatorial properties of the simplicial complex. By generalizing the notion of a tree from graphs to simplicial complexes, we show that ideals associated to trees satisfy sliding depth condition, and therefore have normal and Cohen-Macaulay Rees rings. We also discuss connections with the theory of Stanley-Reisner rings.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Sara Faridi
    • 1
  1. 1.Mathematics Department, George Washington University, Washington, DC 20052. e-mail:

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