On vanishing patterns in j-strands of edge ideals

Abed Abedelfatah*, Eran Nevo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We consider two problems regarding vanishing patterns in the Betti table of edge ideals I over any fixed field. First, we show that the j-strand is connected if j= 3 (for j= 2 this is easy and known), and give examples where the j-strand is not connected for any j> 3. Next, we apply our result on strand connectivity to establish the subadditivity conjecture for edge ideals, ta + b(I) ≤ ta(I) + tb(I) , in case b= 2 , 3 (the case b= 1 is known). Here ti(I) denote the maximal shifts in the minimal free resolution of S / I over its polynomial algebra.

Original languageAmerican English
Pages (from-to)287-295
Number of pages9
JournalJournal of Algebraic Combinatorics
Volume46
Issue number2
DOIs
StatePublished - 1 Sep 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media New York.

Keywords

  • Betti diagram
  • Edge ideal
  • Monomial ideal
  • Simplicial complex
  • Subadditivity

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