On vanishing patterns in j-strands of edge ideals

Abed Abedelfatah; Eran Nevo

doi:10.1007/s10801-017-0747-5

On vanishing patterns in j-strands of edge ideals

Abed Abedelfatah^*
, Eran Nevo

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

10 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, t_a ₊ _b(I) ≤ t_a(I) + t_b(I) , in case b= 2 , 3 (the case b= 1 is known). Here t_i(I) denote the maximal shifts in the minimal free resolution of S / I over its polynomial algebra.

Original language	English
Pages (from-to)	287-295
Number of pages	9
Journal	Journal of Algebraic Combinatorics
Volume	46
Issue number	2
DOIs	https://doi.org/10.1007/s10801-017-0747-5
State	Published - 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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AU - Nevo, Eran

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N2 - 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.

AB - 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.

KW - Betti diagram

KW - Edge ideal

KW - Monomial ideal

KW - Simplicial complex

KW - Subadditivity

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EP - 295

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 2

ER -

On vanishing patterns in j-strands of edge ideals

Abstract

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Keywords

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