Minimal Betti numbers

Christopher Dodd, Andrew Marks, Victor Meyerson, Ben Richert

Research output: Contribution to journalArticlepeer-review


We give conditions for determining the extremal behavior for the (graded) Betti numbers of squarefree monomial ideals. For the case of non-unique minima, we give several conditions which we use to produce infinite families, exponentially growing with dimension, of Hilbert functions which have no smallest (graded) Betti numbers among squarefree monomial ideals and all ideals. For the case of unique minima, we give two families of Hilbert functions, one with exponential and one with linear growth as dimension grows, that have unique minimal Betti numbers among squarefree monomial ideals.

Original languageEnglish (US)
Pages (from-to)759-772
Number of pages14
JournalCommunications in Algebra
Issue number3
StatePublished - Mar 2007
Externally publishedYes


  • Betti numbers
  • Hilbert functions
  • Simplicial complexes
  • Squarefree monomial ideals

ASJC Scopus subject areas

  • Algebra and Number Theory


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