On vanishing patterns in j-strands of edge ideals

2015/10/28 by Abed Abedelfatah, Eran Nevo, Abedelfatah, Abed +1
Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO

paper · pdf · doi:10.48550/arxiv.1510.08192

9 pages

arxiv created 2016/03/02 · arxiv updated 2016/03/03

Abstract

We consider two problems regarding vanishing patterns in the Betti table of edge ideals I in polynomial algebra S. 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, t_a+b≤ t_a+t_b, in case b=2,3 (the case b=1 is known). Here t_i stands for the maximal shifts in the minimal free S-resolution of S/I

Related

• Subadditivity, strand connectivity and multigraded Betti numbers of monomial ideals
• On the linear strand of an edge ideal
• Powers of edge ideals
• Linear strands of edge ideals of multipartite uniform clutters
• Non-vanishing of Betti numbers of edge ideals and complete bipartite subgraphs