A Survey of Stanley–Reisner Theory

  • Christopher A. Francisco
  • Jeffrey Mermin
  • Jay Schweig
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 76)


We survey the Stanley–Reisner correspondence in combinatorial commutative algebra, describing fundamental applications involving Alexander duality, associated primes, f- and h-vectors, and Betti numbers of monomial ideals.


Simplicial Complex Betti Number Hilbert Series Hilbert Function Monomial Ideal 
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We thank the referee for his or her careful reading and helpful comments. This work was partially supported by grants from the Simons Foundation (#199124 to Francisco and #202115 to Mermin).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Christopher A. Francisco
    • 1
  • Jeffrey Mermin
    • 1
  • Jay Schweig
    • 1
  1. 1.Department of MathematicsOklahoma State UniversityStillwaterUSA

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