Specializations of Ferrers ideals

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20 Scopus citations

Abstract

We introduce a specialization technique in order to study monomial ideals that are generated in degree two by using our earlier results about Ferrers ideals. It allows us to describe explicitly a cellular minimal free resolution of various ideals including any strongly stable and any squarefree strongly stable ideal whose minimal generators have degree two. In particular, this shows that threshold graphs can be obtained as specializations of Ferrers graphs, which explains their similar properties.

Original languageEnglish
Pages (from-to)425-437
Number of pages13
JournalJournal of Algebraic Combinatorics
Volume28
Issue number3
DOIs
StatePublished - Nov 2008

Bibliographical note

Funding Information:
Acknowledgements The authors would like to thank Vic Reiner for inspiring discussions and the anonymous referees for their careful reading of the original manuscript. Uwe Nagel gratefully acknowledges partial support from the NSA under grant H98230-07-1-0065.

Keywords

  • Cellular minimal free resolution
  • Ferrers graphs
  • Monomial (edge) ideals
  • Threshold graphs

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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