Combinatorial interpretations of some Boij-Söderberg decompositions

Uwe Nagel, Stephen Sturgeon

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Boij-Söderberg theory shows that the Betti table of a graded module can be written as a linear combination of pure diagrams with integer coefficients. Using Ferrers hypergraphs and simplicial polytopes, we provide interpretations of these coefficients for ideals with a d-linear resolution, their quotient rings, and for Gorenstein rings whose resolution has essentially at most two linear strands. We also establish a structural result on the decomposition in the case of quasi-Gorenstein modules.

Original languageEnglish
Pages (from-to)54-72
Number of pages19
JournalJournal of Algebra
StatePublished - May 1 2013

Bibliographical note

Funding Information:
✩ This work was partially supported by a grant from the Simons Foundation (#208869 to Uwe Nagel) and by the National Security Agency under Grant No. H98230-12-1-0247. The second author also would like to thank MSRI for organizing and funding the summer workshop on commutative algebra in 2011 as well as Daniel Erman for his inspiring lectures. * Corresponding author. E-mail addresses: [email protected] (U. Nagel), [email protected] (S. Sturgeon).


  • Boij-Söderberg theory
  • Ferrers hypergraph
  • Gorenstein ring
  • Linear resolution
  • O-sequence
  • Quasi-Gorenstein module

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Combinatorial interpretations of some Boij-Söderberg decompositions'. Together they form a unique fingerprint.

Cite this