Mathematische Zeitschrift

, Volume 274, Issue 3–4, pp 805–819 | Cite as

Poset embeddings of Hilbert functions



For a standard graded algebra \(R\), we consider embeddings of the poset of Hilbert functions of \(R\)-ideals into the poset of \(R\)-ideals, as a way of classification of Hilbert functions. There are examples of rings for which such embeddings do not exist. We describe how the embedding can be lifted to certain ring extensions, which is then used in the case of polarization and distraction. A version of a theorem of Clements–Lindström is proved. We exhibit a condition on the embedding that ensures that the classification of Hilbert functions is obtained with images of lexicographic segment ideals.


Polynomial Ring Formal Power Series Total Order Lexicographic Order Hilbert Series 
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.



We thank A. Conca and the referee for helpful comments. The computer algebra system Macaulay2 [13] provided valuable assistance in studying examples.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Chennai Mathematical InstituteSiruseriIndia

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